REAL is V179() V180() V181() V185() set
NAT is V179() V180() V181() V182() V183() V184() V185() Element of K6(REAL)
K6(REAL) is set
COMPLEX is V179() V185() set
RAT is V179() V180() V181() V182() V185() set
INT is V179() V180() V181() V182() V183() V185() set
K7(COMPLEX,COMPLEX) is V16() complex-yielding set
K6(K7(COMPLEX,COMPLEX)) is set
K7(K7(COMPLEX,COMPLEX),COMPLEX) is V16() complex-yielding set
K6(K7(K7(COMPLEX,COMPLEX),COMPLEX)) is set
K7(REAL,REAL) is V16() complex-yielding ext-real-valued real-valued set
K6(K7(REAL,REAL)) is set
K7(K7(REAL,REAL),REAL) is V16() complex-yielding ext-real-valued real-valued set
K6(K7(K7(REAL,REAL),REAL)) is set
K7(RAT,RAT) is V16() V20( RAT ) complex-yielding ext-real-valued real-valued set
K6(K7(RAT,RAT)) is set
K7(K7(RAT,RAT),RAT) is V16() V20( RAT ) complex-yielding ext-real-valued real-valued set
K6(K7(K7(RAT,RAT),RAT)) is set
K7(INT,INT) is V16() V20( RAT ) V20( INT ) complex-yielding ext-real-valued real-valued set
K6(K7(INT,INT)) is set
K7(K7(INT,INT),INT) is V16() V20( RAT ) V20( INT ) complex-yielding ext-real-valued real-valued set
K6(K7(K7(INT,INT),INT)) is set
K7(NAT,NAT) is V16() V20( RAT ) V20( INT ) complex-yielding ext-real-valued real-valued natural-valued set
K7(K7(NAT,NAT),NAT) is V16() V20( RAT ) V20( INT ) complex-yielding ext-real-valued real-valued natural-valued set
K6(K7(K7(NAT,NAT),NAT)) is set
omega is V179() V180() V181() V182() V183() V184() V185() set
K6(omega) is set
K6(NAT) is set
K343() is TopStruct
the carrier of K343() is set
1 is non empty ordinal natural V11() real ext-real positive non negative V33() V34() V179() V180() V181() V182() V183() V184() Element of NAT
K7(1,1) is V16() V20( RAT ) V20( INT ) complex-yielding ext-real-valued real-valued natural-valued set
K6(K7(1,1)) is set
K7(K7(1,1),1) is V16() V20( RAT ) V20( INT ) complex-yielding ext-real-valued real-valued natural-valued set
K6(K7(K7(1,1),1)) is set
K7(K7(1,1),REAL) is V16() complex-yielding ext-real-valued real-valued set
K6(K7(K7(1,1),REAL)) is set
2 is non empty ordinal natural V11() real ext-real positive non negative V33() V34() V179() V180() V181() V182() V183() V184() Element of NAT
K7(2,2) is V16() V20( RAT ) V20( INT ) complex-yielding ext-real-valued real-valued natural-valued set
K7(K7(2,2),REAL) is V16() complex-yielding ext-real-valued real-valued set
K6(K7(K7(2,2),REAL)) is set
K514() is non empty V128() L10()
the carrier of K514() is non empty set
K519() is non empty V128() V150() V151() V152() V154() V201() V202() V203() V204() V205() V206() L10()
K520() is non empty V128() V152() V154() V204() V205() V206() M19(K519())
K521() is non empty V128() V150() V152() V154() V204() V205() V206() V207() M22(K519(),K520())
K523() is non empty V128() V150() V152() V154() L10()
K524() is non empty V128() V150() V152() V154() V207() M19(K523())
TOP-REAL 2 is non empty TopSpace-like V126() V191() V192() V209() V210() V211() V212() V213() V214() V215() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL 2) is non empty set
NonZero (TOP-REAL 2) is Element of K6( the carrier of (TOP-REAL 2))
K6( the carrier of (TOP-REAL 2)) is set
[#] (TOP-REAL 2) is non empty non proper non proper closed closed convex Element of K6( the carrier of (TOP-REAL 2))
0. (TOP-REAL 2) is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like V69( TOP-REAL 2) complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
the ZeroF of (TOP-REAL 2) is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
{(0. (TOP-REAL 2))} is non empty V24() set
([#] (TOP-REAL 2)) \ {(0. (TOP-REAL 2))} is Element of K6( the carrier of (TOP-REAL 2))
K7((NonZero (TOP-REAL 2)),(NonZero (TOP-REAL 2))) is V16() set
K6(K7((NonZero (TOP-REAL 2)),(NonZero (TOP-REAL 2)))) is set
K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)) is V16() set
K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2))) is set
{} is empty V16() non-zero V18() V19( NAT ) V20( RAT ) V21() V22() constant V24() V37() FinSequence-like FinSubsequence-like FinSequence-membered complex-yielding ext-real-valued real-valued natural-valued V179() V180() V181() V182() V183() V184() V185() set
the empty V16() non-zero V18() V19( NAT ) V20( RAT ) V21() V22() constant V24() V37() FinSequence-like FinSubsequence-like FinSequence-membered complex-yielding ext-real-valued real-valued natural-valued V179() V180() V181() V182() V183() V184() V185() set is empty V16() non-zero V18() V19( NAT ) V20( RAT ) V21() V22() constant V24() V37() FinSequence-like FinSubsequence-like FinSequence-membered complex-yielding ext-real-valued real-valued natural-valued V179() V180() V181() V182() V183() V184() V185() set
{{},1} is non empty set
3 is non empty ordinal natural V11() real ext-real positive non negative V33() V34() V179() V180() V181() V182() V183() V184() Element of NAT
0 is empty ordinal natural V11() real ext-real non positive non negative V16() non-zero V18() V19( NAT ) V20( RAT ) V21() V22() constant V24() V33() V34() V37() FinSequence-like FinSubsequence-like FinSequence-membered complex-yielding ext-real-valued real-valued natural-valued V179() V180() V181() V182() V183() V184() V185() Element of NAT
sqrt 0 is V11() real ext-real Element of REAL
4 is non empty ordinal natural V11() real ext-real positive non negative V33() V34() V179() V180() V181() V182() V183() V184() Element of NAT
a is ordinal natural V11() real ext-real non negative V33() V34() V179() V180() V181() V182() V183() V184() Element of NAT
TOP-REAL a is non empty TopSpace-like V126() V191() V192() V209() V210() V211() V212() V213() V214() V215() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL a) is non empty set
b is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
b + r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
the U7 of (TOP-REAL a) is V16() V21() V30(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) Element of K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)))
K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)) is V16() set
K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) is V16() set
K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a))) is set
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),b,r) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
b + r is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
b + w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),b,w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
b + w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
b - b is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- b is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- b is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
- 1 is V11() real ext-real non positive set
(- 1) * b is V16() V21() set
K382((TOP-REAL a),b,(- b)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),b,(- b)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
b + (- b) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
b - b is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K448(b) is V16() V21() complex-yielding set
K419(b,K448(b)) is V16() V21() set
(b - b) + r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(b - b),r) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(b - b) + r is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(b + w) - b is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K382((TOP-REAL a),(b + w),(- b)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(b + w),(- b)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(b + w) + (- b) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(b + w) - b is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K419((b + w),K448(b)) is V16() V21() set
0. (TOP-REAL a) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like V69( TOP-REAL a) complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
the ZeroF of (TOP-REAL a) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(b - b) + w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(b - b),w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(b - b) + w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(0. (TOP-REAL a)) + w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(0. (TOP-REAL a)),w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(0. (TOP-REAL a)) + w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
a is ordinal natural V11() real ext-real non negative V33() V34() V179() V180() V181() V182() V183() V184() Element of NAT
TOP-REAL a is non empty TopSpace-like V126() V191() V192() V209() V210() V211() V212() V213() V214() V215() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL a) is non empty set
1.REAL a is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
1* a is V16() V19( NAT ) V20( REAL ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL a
REAL a is non empty V24() FinSequence-membered FinSequenceSet of REAL
a -tuples_on REAL is V24() FinSequence-membered FinSequenceSet of REAL
a |-> 1 is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of a -tuples_on REAL
b is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
b + (1.REAL a) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
the U7 of (TOP-REAL a) is V16() V21() V30(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) Element of K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)))
K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)) is V16() set
K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) is V16() set
K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a))) is set
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),b,(1.REAL a)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
b + (1.REAL a) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
0.REAL a is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
a |-> 0 is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of a -tuples_on REAL
0. (TOP-REAL a) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like V69( TOP-REAL a) complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
the ZeroF of (TOP-REAL a) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
b + (0. (TOP-REAL a)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),b,(0. (TOP-REAL a))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
b + (0. (TOP-REAL a)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
a is ordinal natural V11() real ext-real non negative V33() V34() V179() V180() V181() V182() V183() V184() Element of NAT
TOP-REAL a is non empty TopSpace-like V126() V191() V192() V209() V210() V211() V212() V213() V214() V215() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL a) is non empty set
b is V11() real ext-real set
1 - b is V11() real ext-real Element of REAL
- b is V11() real ext-real set
1 + (- b) is V11() real ext-real set
r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(1 - b) * r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(1 - b) * r is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
b * w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
b * w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - b) * r) + (b * w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
the U7 of (TOP-REAL a) is V16() V21() V30(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) Element of K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)))
K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)) is V16() set
K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) is V16() set
K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a))) is set
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 - b) * r),(b * w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - b) * r) + (b * w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
s is set
0. (TOP-REAL a) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like V69( TOP-REAL a) complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
the ZeroF of (TOP-REAL a) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(((1 - b) * r) + (b * w)) - r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- r is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
- 1 is V11() real ext-real non positive set
(- 1) * r is V16() V21() set
K382((TOP-REAL a),(((1 - b) * r) + (b * w)),(- r)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(((1 - b) * r) + (b * w)),(- r)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(((1 - b) * r) + (b * w)) + (- r) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((1 - b) * r) + (b * w)) - r is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K448(r) is V16() V21() complex-yielding set
K419((((1 - b) * r) + (b * w)),K448(r)) is V16() V21() set
((1 - b) * r) - r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K382((TOP-REAL a),((1 - b) * r),(- r)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 - b) * r),(- r)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - b) * r) + (- r) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - b) * r) - r is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K419(((1 - b) * r),K448(r)) is V16() V21() set
(((1 - b) * r) - r) + (b * w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(((1 - b) * r) - r),(b * w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(((1 - b) * r) - r) + (b * w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
1 * r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
1 * r is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - b) * r) - (1 * r) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- (1 * r) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- (1 * r) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(- 1) * (1 * r) is V16() V21() set
K382((TOP-REAL a),((1 - b) * r),(- (1 * r))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 - b) * r),(- (1 * r))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - b) * r) + (- (1 * r)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - b) * r) - (1 * r) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K448((1 * r)) is V16() V21() complex-yielding set
K419(((1 - b) * r),K448((1 * r))) is V16() V21() set
(((1 - b) * r) - (1 * r)) + (b * w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(((1 - b) * r) - (1 * r)),(b * w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(((1 - b) * r) - (1 * r)) + (b * w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(1 - b) - 1 is V11() real ext-real Element of REAL
(1 - b) + (- 1) is V11() real ext-real set
((1 - b) - 1) * r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - b) - 1) * r is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((1 - b) - 1) * r) + (b * w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(((1 - b) - 1) * r),(b * w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(((1 - b) - 1) * r) + (b * w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
b * r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
b * r is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(b * w) - (b * r) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- (b * r) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- (b * r) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(- 1) * (b * r) is V16() V21() set
K382((TOP-REAL a),(b * w),(- (b * r))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(b * w),(- (b * r))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(b * w) + (- (b * r)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(b * w) - (b * r) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K448((b * r)) is V16() V21() complex-yielding set
K419((b * w),K448((b * r))) is V16() V21() set
w - r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K382((TOP-REAL a),w,(- r)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),w,(- r)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
w + (- r) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
w - r is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K419(w,K448(r)) is V16() V21() set
b * (w - r) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
b * (w - r) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
0 * w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
0 * w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
r + (0 * w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),r,(0 * w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
r + (0 * w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
r + (0. (TOP-REAL a)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),r,(0. (TOP-REAL a))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
r + (0. (TOP-REAL a)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(1 - b) + b is V11() real ext-real Element of REAL
((1 - b) + b) * r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - b) + b) * r is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((1 - b) * r) + (b * w)) - w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(- 1) * w is V16() V21() set
K382((TOP-REAL a),(((1 - b) * r) + (b * w)),(- w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(((1 - b) * r) + (b * w)),(- w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(((1 - b) * r) + (b * w)) + (- w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((1 - b) * r) + (b * w)) - w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K448(w) is V16() V21() complex-yielding set
K419((((1 - b) * r) + (b * w)),K448(w)) is V16() V21() set
(b * w) - w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K382((TOP-REAL a),(b * w),(- w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(b * w),(- w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(b * w) + (- w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(b * w) - w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K419((b * w),K448(w)) is V16() V21() set
((1 - b) * r) + ((b * w) - w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 - b) * r),((b * w) - w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - b) * r) + ((b * w) - w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
- 1 is V11() real ext-real non positive Element of REAL
(- 1) * w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(- 1) * w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(b * w) + ((- 1) * w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(b * w),((- 1) * w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(b * w) + ((- 1) * w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - b) * r) + ((b * w) + ((- 1) * w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 - b) * r),((b * w) + ((- 1) * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - b) * r) + ((b * w) + ((- 1) * w)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(- 1) + b is V11() real ext-real Element of REAL
((- 1) + b) * w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((- 1) + b) * w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - b) * r) + (((- 1) + b) * w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 - b) * r),(((- 1) + b) * w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - b) * r) + (((- 1) + b) * w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
- (1 - b) is V11() real ext-real Element of REAL
(- (1 - b)) * w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(- (1 - b)) * w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - b) * r) + ((- (1 - b)) * w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 - b) * r),((- (1 - b)) * w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - b) * r) + ((- (1 - b)) * w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(1 - b) * w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(1 - b) * w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - b) * r) - ((1 - b) * w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- ((1 - b) * w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- ((1 - b) * w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(- 1) * ((1 - b) * w) is V16() V21() set
K382((TOP-REAL a),((1 - b) * r),(- ((1 - b) * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 - b) * r),(- ((1 - b) * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - b) * r) + (- ((1 - b) * w)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - b) * r) - ((1 - b) * w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K448(((1 - b) * w)) is V16() V21() complex-yielding set
K419(((1 - b) * r),K448(((1 - b) * w))) is V16() V21() set
r - w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K382((TOP-REAL a),r,(- w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),r,(- w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
r + (- w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
r - w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K419(r,K448(w)) is V16() V21() set
(1 - b) * (r - w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(1 - b) * (r - w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(1 - b) + b is V11() real ext-real Element of REAL
0 + b is V11() real ext-real Element of REAL
1 * w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
1 * w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(0. (TOP-REAL a)) + (1 * w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(0. (TOP-REAL a)),(1 * w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(0. (TOP-REAL a)) + (1 * w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - b) + b) * w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - b) + b) * w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
a is V16() V19( NAT ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued set
|.a.| is V11() real ext-real non negative Element of REAL
sqr a is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt (a,a) is V16() V21() set
Sum (sqr a) is V11() real ext-real Element of REAL
sqrt (Sum (sqr a)) is V11() real ext-real Element of REAL
|.a.| ^2 is V11() real ext-real Element of REAL
|.a.| * |.a.| is V11() real ext-real non negative set
a is V11() real ext-real set
b is non empty Reflexive discerning V103() triangle MetrStruct
the carrier of b is non empty set
r is Element of the carrier of b
w is Element of the carrier of b
s is Element of the carrier of b
cl_Ball (s,a) is Element of K6( the carrier of b)
K6( the carrier of b) is set
{s} is non empty set
a is ordinal natural V11() real ext-real non negative set
TOP-REAL a is non empty TopSpace-like V126() V191() V192() V209() V210() V211() V212() V213() V214() V215() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL a) is non empty set
r is V11() real ext-real set
b is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
{ b1 where b1 is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a) : not r <= |.(b1 - b).| } is set
K6( the carrier of (TOP-REAL a)) is set
w is set
s is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
s - b is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- b is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- b is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
- 1 is V11() real ext-real non positive set
(- 1) * b is V16() V21() set
K382((TOP-REAL a),s,(- b)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
the U7 of (TOP-REAL a) is V16() V21() V30(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) Element of K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)))
K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)) is V16() set
K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) is V16() set
K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a))) is set
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),s,(- b)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
s + (- b) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
s - b is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K448(b) is V16() V21() complex-yielding set
K419(s,K448(b)) is V16() V21() set
|.(s - b).| is V11() real ext-real non negative Element of REAL
sqr (s - b) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt ((s - b),(s - b)) is V16() V21() set
Sum (sqr (s - b)) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (s - b))) is V11() real ext-real Element of REAL
{ b1 where b1 is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a) : |.(b1 - b).| <= r } is set
w is set
s is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
s - b is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- b is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- b is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
- 1 is V11() real ext-real non positive set
(- 1) * b is V16() V21() set
K382((TOP-REAL a),s,(- b)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
the U7 of (TOP-REAL a) is V16() V21() V30(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) Element of K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)))
K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)) is V16() set
K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) is V16() set
K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a))) is set
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),s,(- b)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
s + (- b) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
s - b is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K448(b) is V16() V21() complex-yielding set
K419(s,K448(b)) is V16() V21() set
|.(s - b).| is V11() real ext-real non negative Element of REAL
sqr (s - b) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt ((s - b),(s - b)) is V16() V21() set
Sum (sqr (s - b)) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (s - b))) is V11() real ext-real Element of REAL
{ b1 where b1 is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a) : |.(b1 - b).| = r } is set
w is set
s is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
s - b is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- b is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- b is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
- 1 is V11() real ext-real non positive set
(- 1) * b is V16() V21() set
K382((TOP-REAL a),s,(- b)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
the U7 of (TOP-REAL a) is V16() V21() V30(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) Element of K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)))
K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)) is V16() set
K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) is V16() set
K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a))) is set
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),s,(- b)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
s + (- b) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
s - b is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K448(b) is V16() V21() complex-yielding set
K419(s,K448(b)) is V16() V21() set
|.(s - b).| is V11() real ext-real non negative Element of REAL
sqr (s - b) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt ((s - b),(s - b)) is V16() V21() set
Sum (sqr (s - b)) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (s - b))) is V11() real ext-real Element of REAL
a is ordinal natural V11() real ext-real non negative V33() V34() V179() V180() V181() V182() V183() V184() Element of NAT
TOP-REAL a is non empty TopSpace-like V126() V191() V192() V209() V210() V211() V212() V213() V214() V215() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL a) is non empty set
b is V11() real ext-real set
r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(a,w,b) is Element of K6( the carrier of (TOP-REAL a))
K6( the carrier of (TOP-REAL a)) is set
{ b1 where b1 is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a) : not b <= |.(b1 - w).| } is set
r - w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
- 1 is V11() real ext-real non positive set
(- 1) * w is V16() V21() set
K382((TOP-REAL a),r,(- w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
the U7 of (TOP-REAL a) is V16() V21() V30(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) Element of K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)))
K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)) is V16() set
K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) is V16() set
K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a))) is set
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),r,(- w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
r + (- w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
r - w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K448(w) is V16() V21() complex-yielding set
K419(r,K448(w)) is V16() V21() set
|.(r - w).| is V11() real ext-real non negative Element of REAL
sqr (r - w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt ((r - w),(r - w)) is V16() V21() set
Sum (sqr (r - w)) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (r - w))) is V11() real ext-real Element of REAL
s is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
s - w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K382((TOP-REAL a),s,(- w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),s,(- w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
s + (- w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
s - w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K419(s,K448(w)) is V16() V21() set
|.(s - w).| is V11() real ext-real non negative Element of REAL
sqr (s - w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt ((s - w),(s - w)) is V16() V21() set
Sum (sqr (s - w)) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (s - w))) is V11() real ext-real Element of REAL
a is ordinal natural V11() real ext-real non negative V33() V34() V179() V180() V181() V182() V183() V184() Element of NAT
TOP-REAL a is non empty TopSpace-like V126() V191() V192() V209() V210() V211() V212() V213() V214() V215() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL a) is non empty set
b is V11() real ext-real set
r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(a,w,b) is Element of K6( the carrier of (TOP-REAL a))
K6( the carrier of (TOP-REAL a)) is set
{ b1 where b1 is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a) : |.(b1 - w).| <= b } is set
r - w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
- 1 is V11() real ext-real non positive set
(- 1) * w is V16() V21() set
K382((TOP-REAL a),r,(- w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
the U7 of (TOP-REAL a) is V16() V21() V30(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) Element of K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)))
K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)) is V16() set
K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) is V16() set
K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a))) is set
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),r,(- w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
r + (- w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
r - w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K448(w) is V16() V21() complex-yielding set
K419(r,K448(w)) is V16() V21() set
|.(r - w).| is V11() real ext-real non negative Element of REAL
sqr (r - w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt ((r - w),(r - w)) is V16() V21() set
Sum (sqr (r - w)) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (r - w))) is V11() real ext-real Element of REAL
s is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
s - w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K382((TOP-REAL a),s,(- w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),s,(- w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
s + (- w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
s - w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K419(s,K448(w)) is V16() V21() set
|.(s - w).| is V11() real ext-real non negative Element of REAL
sqr (s - w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt ((s - w),(s - w)) is V16() V21() set
Sum (sqr (s - w)) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (s - w))) is V11() real ext-real Element of REAL
a is ordinal natural V11() real ext-real non negative V33() V34() V179() V180() V181() V182() V183() V184() Element of NAT
TOP-REAL a is non empty TopSpace-like V126() V191() V192() V209() V210() V211() V212() V213() V214() V215() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL a) is non empty set
b is V11() real ext-real set
r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(a,w,b) is Element of K6( the carrier of (TOP-REAL a))
K6( the carrier of (TOP-REAL a)) is set
{ b1 where b1 is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a) : |.(b1 - w).| = b } is set
r - w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
- 1 is V11() real ext-real non positive set
(- 1) * w is V16() V21() set
K382((TOP-REAL a),r,(- w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
the U7 of (TOP-REAL a) is V16() V21() V30(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) Element of K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)))
K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)) is V16() set
K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) is V16() set
K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a))) is set
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),r,(- w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
r + (- w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
r - w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K448(w) is V16() V21() complex-yielding set
K419(r,K448(w)) is V16() V21() set
|.(r - w).| is V11() real ext-real non negative Element of REAL
sqr (r - w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt ((r - w),(r - w)) is V16() V21() set
Sum (sqr (r - w)) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (r - w))) is V11() real ext-real Element of REAL
s is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
s - w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K382((TOP-REAL a),s,(- w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),s,(- w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
s + (- w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
s - w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K419(s,K448(w)) is V16() V21() set
|.(s - w).| is V11() real ext-real non negative Element of REAL
sqr (s - w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt ((s - w),(s - w)) is V16() V21() set
Sum (sqr (s - w)) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (s - w))) is V11() real ext-real Element of REAL
a is ordinal natural V11() real ext-real non negative V33() V34() V179() V180() V181() V182() V183() V184() Element of NAT
TOP-REAL a is non empty TopSpace-like V126() V191() V192() V209() V210() V211() V212() V213() V214() V215() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL a) is non empty set
0. (TOP-REAL a) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like V69( TOP-REAL a) complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
the ZeroF of (TOP-REAL a) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
b is V11() real ext-real set
(a,(0. (TOP-REAL a)),b) is Element of K6( the carrier of (TOP-REAL a))
K6( the carrier of (TOP-REAL a)) is set
{ b1 where b1 is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a) : not b <= |.(b1 - (0. (TOP-REAL a))).| } is set
r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
|.r.| is V11() real ext-real non negative Element of REAL
sqr r is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt (r,r) is V16() V21() set
Sum (sqr r) is V11() real ext-real Element of REAL
sqrt (Sum (sqr r)) is V11() real ext-real Element of REAL
r - (0. (TOP-REAL a)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- (0. (TOP-REAL a)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- (0. (TOP-REAL a)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
- 1 is V11() real ext-real non positive set
(- 1) * (0. (TOP-REAL a)) is V16() V21() set
K382((TOP-REAL a),r,(- (0. (TOP-REAL a)))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
the U7 of (TOP-REAL a) is V16() V21() V30(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) Element of K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)))
K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)) is V16() set
K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) is V16() set
K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a))) is set
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),r,(- (0. (TOP-REAL a)))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
r + (- (0. (TOP-REAL a))) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
r - (0. (TOP-REAL a)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K448((0. (TOP-REAL a))) is V16() V21() complex-yielding set
K419(r,K448((0. (TOP-REAL a)))) is V16() V21() set
|.(r - (0. (TOP-REAL a))).| is V11() real ext-real non negative Element of REAL
sqr (r - (0. (TOP-REAL a))) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt ((r - (0. (TOP-REAL a))),(r - (0. (TOP-REAL a)))) is V16() V21() set
Sum (sqr (r - (0. (TOP-REAL a)))) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (r - (0. (TOP-REAL a))))) is V11() real ext-real Element of REAL
a is ordinal natural V11() real ext-real non negative V33() V34() V179() V180() V181() V182() V183() V184() Element of NAT
TOP-REAL a is non empty TopSpace-like V126() V191() V192() V209() V210() V211() V212() V213() V214() V215() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL a) is non empty set
0. (TOP-REAL a) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like V69( TOP-REAL a) complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
the ZeroF of (TOP-REAL a) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
b is V11() real ext-real set
(a,(0. (TOP-REAL a)),b) is Element of K6( the carrier of (TOP-REAL a))
K6( the carrier of (TOP-REAL a)) is set
{ b1 where b1 is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a) : |.(b1 - (0. (TOP-REAL a))).| <= b } is set
r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
|.r.| is V11() real ext-real non negative Element of REAL
sqr r is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt (r,r) is V16() V21() set
Sum (sqr r) is V11() real ext-real Element of REAL
sqrt (Sum (sqr r)) is V11() real ext-real Element of REAL
r - (0. (TOP-REAL a)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- (0. (TOP-REAL a)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- (0. (TOP-REAL a)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
- 1 is V11() real ext-real non positive set
(- 1) * (0. (TOP-REAL a)) is V16() V21() set
K382((TOP-REAL a),r,(- (0. (TOP-REAL a)))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
the U7 of (TOP-REAL a) is V16() V21() V30(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) Element of K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)))
K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)) is V16() set
K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) is V16() set
K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a))) is set
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),r,(- (0. (TOP-REAL a)))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
r + (- (0. (TOP-REAL a))) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
r - (0. (TOP-REAL a)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K448((0. (TOP-REAL a))) is V16() V21() complex-yielding set
K419(r,K448((0. (TOP-REAL a)))) is V16() V21() set
|.(r - (0. (TOP-REAL a))).| is V11() real ext-real non negative Element of REAL
sqr (r - (0. (TOP-REAL a))) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt ((r - (0. (TOP-REAL a))),(r - (0. (TOP-REAL a)))) is V16() V21() set
Sum (sqr (r - (0. (TOP-REAL a)))) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (r - (0. (TOP-REAL a))))) is V11() real ext-real Element of REAL
a is ordinal natural V11() real ext-real non negative V33() V34() V179() V180() V181() V182() V183() V184() Element of NAT
TOP-REAL a is non empty TopSpace-like V126() V191() V192() V209() V210() V211() V212() V213() V214() V215() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL a) is non empty set
0. (TOP-REAL a) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like V69( TOP-REAL a) complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
the ZeroF of (TOP-REAL a) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
b is V11() real ext-real set
(a,(0. (TOP-REAL a)),b) is Element of K6( the carrier of (TOP-REAL a))
K6( the carrier of (TOP-REAL a)) is set
{ b1 where b1 is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a) : |.(b1 - (0. (TOP-REAL a))).| = b } is set
r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
|.r.| is V11() real ext-real non negative Element of REAL
sqr r is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt (r,r) is V16() V21() set
Sum (sqr r) is V11() real ext-real Element of REAL
sqrt (Sum (sqr r)) is V11() real ext-real Element of REAL
r - (0. (TOP-REAL a)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- (0. (TOP-REAL a)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- (0. (TOP-REAL a)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
- 1 is V11() real ext-real non positive set
(- 1) * (0. (TOP-REAL a)) is V16() V21() set
K382((TOP-REAL a),r,(- (0. (TOP-REAL a)))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
the U7 of (TOP-REAL a) is V16() V21() V30(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) Element of K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)))
K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)) is V16() set
K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) is V16() set
K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a))) is set
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),r,(- (0. (TOP-REAL a)))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
r + (- (0. (TOP-REAL a))) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
r - (0. (TOP-REAL a)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K448((0. (TOP-REAL a))) is V16() V21() complex-yielding set
K419(r,K448((0. (TOP-REAL a)))) is V16() V21() set
|.(r - (0. (TOP-REAL a))).| is V11() real ext-real non negative Element of REAL
sqr (r - (0. (TOP-REAL a))) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt ((r - (0. (TOP-REAL a))),(r - (0. (TOP-REAL a)))) is V16() V21() set
Sum (sqr (r - (0. (TOP-REAL a)))) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (r - (0. (TOP-REAL a))))) is V11() real ext-real Element of REAL
a is ordinal natural V11() real ext-real non negative V33() V34() V179() V180() V181() V182() V183() V184() Element of NAT
TOP-REAL a is non empty TopSpace-like V126() V191() V192() V209() V210() V211() V212() V213() V214() V215() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL a) is non empty set
Euclid a is non empty strict Reflexive discerning V103() triangle MetrStruct
REAL a is non empty V24() FinSequence-membered FinSequenceSet of REAL
a -tuples_on REAL is V24() FinSequence-membered FinSequenceSet of REAL
Pitag_dist a is V16() V21() V30(K7((REAL a),(REAL a)), REAL ) complex-yielding ext-real-valued real-valued Element of K6(K7(K7((REAL a),(REAL a)),REAL))
K7((REAL a),(REAL a)) is V16() set
K7(K7((REAL a),(REAL a)),REAL) is V16() complex-yielding ext-real-valued real-valued set
K6(K7(K7((REAL a),(REAL a)),REAL)) is set
MetrStruct(# (REAL a),(Pitag_dist a) #) is strict MetrStruct
the carrier of (Euclid a) is non empty set
b is V11() real ext-real set
r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(a,r,b) is Element of K6( the carrier of (TOP-REAL a))
K6( the carrier of (TOP-REAL a)) is set
{ b1 where b1 is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a) : not b <= |.(b1 - r).| } is set
w is Element of the carrier of (Euclid a)
Ball (w,b) is bounded Element of K6( the carrier of (Euclid a))
K6( the carrier of (Euclid a)) is set
s is set
t is Element of the carrier of (Euclid a)
dist (t,w) is V11() real ext-real Element of REAL
G is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
G - r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- r is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
- 1 is V11() real ext-real non positive set
(- 1) * r is V16() V21() set
K382((TOP-REAL a),G,(- r)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
the U7 of (TOP-REAL a) is V16() V21() V30(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) Element of K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)))
K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)) is V16() set
K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) is V16() set
K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a))) is set
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),G,(- r)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
G + (- r) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
G - r is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K448(r) is V16() V21() complex-yielding set
K419(G,K448(r)) is V16() V21() set
|.(G - r).| is V11() real ext-real non negative Element of REAL
sqr (G - r) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt ((G - r),(G - r)) is V16() V21() set
Sum (sqr (G - r)) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (G - r))) is V11() real ext-real Element of REAL
s is set
t is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
t - r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K382((TOP-REAL a),t,(- r)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),t,(- r)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
t + (- r) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
t - r is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K419(t,K448(r)) is V16() V21() set
|.(t - r).| is V11() real ext-real non negative Element of REAL
sqr (t - r) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt ((t - r),(t - r)) is V16() V21() set
Sum (sqr (t - r)) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (t - r))) is V11() real ext-real Element of REAL
G is Element of the carrier of (Euclid a)
dist (G,w) is V11() real ext-real Element of REAL
a is ordinal natural V11() real ext-real non negative V33() V34() V179() V180() V181() V182() V183() V184() Element of NAT
TOP-REAL a is non empty TopSpace-like V126() V191() V192() V209() V210() V211() V212() V213() V214() V215() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL a) is non empty set
Euclid a is non empty strict Reflexive discerning V103() triangle MetrStruct
REAL a is non empty V24() FinSequence-membered FinSequenceSet of REAL
a -tuples_on REAL is V24() FinSequence-membered FinSequenceSet of REAL
Pitag_dist a is V16() V21() V30(K7((REAL a),(REAL a)), REAL ) complex-yielding ext-real-valued real-valued Element of K6(K7(K7((REAL a),(REAL a)),REAL))
K7((REAL a),(REAL a)) is V16() set
K7(K7((REAL a),(REAL a)),REAL) is V16() complex-yielding ext-real-valued real-valued set
K6(K7(K7((REAL a),(REAL a)),REAL)) is set
MetrStruct(# (REAL a),(Pitag_dist a) #) is strict MetrStruct
the carrier of (Euclid a) is non empty set
b is V11() real ext-real set
r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(a,r,b) is Element of K6( the carrier of (TOP-REAL a))
K6( the carrier of (TOP-REAL a)) is set
{ b1 where b1 is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a) : |.(b1 - r).| <= b } is set
w is Element of the carrier of (Euclid a)
cl_Ball (w,b) is Element of K6( the carrier of (Euclid a))
K6( the carrier of (Euclid a)) is set
s is set
t is Element of the carrier of (Euclid a)
dist (t,w) is V11() real ext-real Element of REAL
G is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
G - r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- r is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
- 1 is V11() real ext-real non positive set
(- 1) * r is V16() V21() set
K382((TOP-REAL a),G,(- r)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
the U7 of (TOP-REAL a) is V16() V21() V30(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) Element of K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)))
K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)) is V16() set
K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) is V16() set
K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a))) is set
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),G,(- r)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
G + (- r) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
G - r is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K448(r) is V16() V21() complex-yielding set
K419(G,K448(r)) is V16() V21() set
|.(G - r).| is V11() real ext-real non negative Element of REAL
sqr (G - r) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt ((G - r),(G - r)) is V16() V21() set
Sum (sqr (G - r)) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (G - r))) is V11() real ext-real Element of REAL
s is set
t is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
t - r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K382((TOP-REAL a),t,(- r)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),t,(- r)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
t + (- r) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
t - r is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K419(t,K448(r)) is V16() V21() set
|.(t - r).| is V11() real ext-real non negative Element of REAL
sqr (t - r) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt ((t - r),(t - r)) is V16() V21() set
Sum (sqr (t - r)) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (t - r))) is V11() real ext-real Element of REAL
G is Element of the carrier of (Euclid a)
dist (G,w) is V11() real ext-real Element of REAL
a is ordinal natural V11() real ext-real non negative V33() V34() V179() V180() V181() V182() V183() V184() Element of NAT
TOP-REAL a is non empty TopSpace-like V126() V191() V192() V209() V210() V211() V212() V213() V214() V215() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL a) is non empty set
Euclid a is non empty strict Reflexive discerning V103() triangle MetrStruct
REAL a is non empty V24() FinSequence-membered FinSequenceSet of REAL
a -tuples_on REAL is V24() FinSequence-membered FinSequenceSet of REAL
Pitag_dist a is V16() V21() V30(K7((REAL a),(REAL a)), REAL ) complex-yielding ext-real-valued real-valued Element of K6(K7(K7((REAL a),(REAL a)),REAL))
K7((REAL a),(REAL a)) is V16() set
K7(K7((REAL a),(REAL a)),REAL) is V16() complex-yielding ext-real-valued real-valued set
K6(K7(K7((REAL a),(REAL a)),REAL)) is set
MetrStruct(# (REAL a),(Pitag_dist a) #) is strict MetrStruct
the carrier of (Euclid a) is non empty set
b is V11() real ext-real set
r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(a,r,b) is Element of K6( the carrier of (TOP-REAL a))
K6( the carrier of (TOP-REAL a)) is set
{ b1 where b1 is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a) : |.(b1 - r).| = b } is set
w is Element of the carrier of (Euclid a)
Sphere (w,b) is Element of K6( the carrier of (Euclid a))
K6( the carrier of (Euclid a)) is set
s is set
t is Element of the carrier of (Euclid a)
dist (t,w) is V11() real ext-real Element of REAL
G is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
G - r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- r is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
- 1 is V11() real ext-real non positive set
(- 1) * r is V16() V21() set
K382((TOP-REAL a),G,(- r)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
the U7 of (TOP-REAL a) is V16() V21() V30(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) Element of K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)))
K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)) is V16() set
K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) is V16() set
K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a))) is set
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),G,(- r)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
G + (- r) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
G - r is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K448(r) is V16() V21() complex-yielding set
K419(G,K448(r)) is V16() V21() set
|.(G - r).| is V11() real ext-real non negative Element of REAL
sqr (G - r) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt ((G - r),(G - r)) is V16() V21() set
Sum (sqr (G - r)) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (G - r))) is V11() real ext-real Element of REAL
s is set
t is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
t - r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K382((TOP-REAL a),t,(- r)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),t,(- r)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
t + (- r) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
t - r is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K419(t,K448(r)) is V16() V21() set
|.(t - r).| is V11() real ext-real non negative Element of REAL
sqr (t - r) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt ((t - r),(t - r)) is V16() V21() set
Sum (sqr (t - r)) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (t - r))) is V11() real ext-real Element of REAL
G is Element of the carrier of (Euclid a)
dist (G,w) is V11() real ext-real Element of REAL
a is ordinal natural V11() real ext-real non negative V33() V34() V179() V180() V181() V182() V183() V184() Element of NAT
TOP-REAL a is non empty TopSpace-like V126() V191() V192() V209() V210() V211() V212() V213() V214() V215() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL a) is non empty set
b is V11() real ext-real set
r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(a,r,b) is Element of K6( the carrier of (TOP-REAL a))
K6( the carrier of (TOP-REAL a)) is set
{ b1 where b1 is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a) : not b <= |.(b1 - r).| } is set
(a,r,b) is Element of K6( the carrier of (TOP-REAL a))
{ b1 where b1 is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a) : |.(b1 - r).| <= b } is set
Euclid a is non empty strict Reflexive discerning V103() triangle MetrStruct
REAL a is non empty V24() FinSequence-membered FinSequenceSet of REAL
a -tuples_on REAL is V24() FinSequence-membered FinSequenceSet of REAL
Pitag_dist a is V16() V21() V30(K7((REAL a),(REAL a)), REAL ) complex-yielding ext-real-valued real-valued Element of K6(K7(K7((REAL a),(REAL a)),REAL))
K7((REAL a),(REAL a)) is V16() set
K7(K7((REAL a),(REAL a)),REAL) is V16() complex-yielding ext-real-valued real-valued set
K6(K7(K7((REAL a),(REAL a)),REAL)) is set
MetrStruct(# (REAL a),(Pitag_dist a) #) is strict MetrStruct
the carrier of (Euclid a) is non empty set
w is Element of the carrier of (Euclid a)
Ball (w,b) is bounded Element of K6( the carrier of (Euclid a))
K6( the carrier of (Euclid a)) is set
cl_Ball (w,b) is Element of K6( the carrier of (Euclid a))
a is ordinal natural V11() real ext-real non negative V33() V34() V179() V180() V181() V182() V183() V184() Element of NAT
TOP-REAL a is non empty TopSpace-like V126() V191() V192() V209() V210() V211() V212() V213() V214() V215() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL a) is non empty set
b is V11() real ext-real set
r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(a,r,b) is Element of K6( the carrier of (TOP-REAL a))
K6( the carrier of (TOP-REAL a)) is set
{ b1 where b1 is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a) : |.(b1 - r).| = b } is set
(a,r,b) is Element of K6( the carrier of (TOP-REAL a))
{ b1 where b1 is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a) : |.(b1 - r).| <= b } is set
Euclid a is non empty strict Reflexive discerning V103() triangle MetrStruct
REAL a is non empty V24() FinSequence-membered FinSequenceSet of REAL
a -tuples_on REAL is V24() FinSequence-membered FinSequenceSet of REAL
Pitag_dist a is V16() V21() V30(K7((REAL a),(REAL a)), REAL ) complex-yielding ext-real-valued real-valued Element of K6(K7(K7((REAL a),(REAL a)),REAL))
K7((REAL a),(REAL a)) is V16() set
K7(K7((REAL a),(REAL a)),REAL) is V16() complex-yielding ext-real-valued real-valued set
K6(K7(K7((REAL a),(REAL a)),REAL)) is set
MetrStruct(# (REAL a),(Pitag_dist a) #) is strict MetrStruct
the carrier of (Euclid a) is non empty set
w is Element of the carrier of (Euclid a)
Sphere (w,b) is Element of K6( the carrier of (Euclid a))
K6( the carrier of (Euclid a)) is set
cl_Ball (w,b) is Element of K6( the carrier of (Euclid a))
a is ordinal natural V11() real ext-real non negative V33() V34() V179() V180() V181() V182() V183() V184() Element of NAT
TOP-REAL a is non empty TopSpace-like V126() V191() V192() V209() V210() V211() V212() V213() V214() V215() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL a) is non empty set
b is V11() real ext-real set
r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(a,r,b) is Element of K6( the carrier of (TOP-REAL a))
K6( the carrier of (TOP-REAL a)) is set
{ b1 where b1 is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a) : not b <= |.(b1 - r).| } is set
(a,r,b) is Element of K6( the carrier of (TOP-REAL a))
{ b1 where b1 is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a) : |.(b1 - r).| = b } is set
(a,r,b) \/ (a,r,b) is Element of K6( the carrier of (TOP-REAL a))
(a,r,b) is Element of K6( the carrier of (TOP-REAL a))
{ b1 where b1 is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a) : |.(b1 - r).| <= b } is set
Euclid a is non empty strict Reflexive discerning V103() triangle MetrStruct
REAL a is non empty V24() FinSequence-membered FinSequenceSet of REAL
a -tuples_on REAL is V24() FinSequence-membered FinSequenceSet of REAL
Pitag_dist a is V16() V21() V30(K7((REAL a),(REAL a)), REAL ) complex-yielding ext-real-valued real-valued Element of K6(K7(K7((REAL a),(REAL a)),REAL))
K7((REAL a),(REAL a)) is V16() set
K7(K7((REAL a),(REAL a)),REAL) is V16() complex-yielding ext-real-valued real-valued set
K6(K7(K7((REAL a),(REAL a)),REAL)) is set
MetrStruct(# (REAL a),(Pitag_dist a) #) is strict MetrStruct
the carrier of (Euclid a) is non empty set
w is Element of the carrier of (Euclid a)
cl_Ball (w,b) is Element of K6( the carrier of (Euclid a))
K6( the carrier of (Euclid a)) is set
Sphere (w,b) is Element of K6( the carrier of (Euclid a))
Ball (w,b) is bounded Element of K6( the carrier of (Euclid a))
a is ordinal natural V11() real ext-real non negative V33() V34() V179() V180() V181() V182() V183() V184() Element of NAT
TOP-REAL a is non empty TopSpace-like V126() V191() V192() V209() V210() V211() V212() V213() V214() V215() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL a) is non empty set
b is V11() real ext-real set
r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(a,r,b) is Element of K6( the carrier of (TOP-REAL a))
K6( the carrier of (TOP-REAL a)) is set
{ b1 where b1 is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a) : not b <= |.(b1 - r).| } is set
(a,r,b) is Element of K6( the carrier of (TOP-REAL a))
{ b1 where b1 is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a) : |.(b1 - r).| = b } is set
w is set
s is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
s - r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- r is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
- 1 is V11() real ext-real non positive set
(- 1) * r is V16() V21() set
K382((TOP-REAL a),s,(- r)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
the U7 of (TOP-REAL a) is V16() V21() V30(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) Element of K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)))
K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)) is V16() set
K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) is V16() set
K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a))) is set
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),s,(- r)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
s + (- r) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
s - r is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K448(r) is V16() V21() complex-yielding set
K419(s,K448(r)) is V16() V21() set
|.(s - r).| is V11() real ext-real non negative Element of REAL
sqr (s - r) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt ((s - r),(s - r)) is V16() V21() set
Sum (sqr (s - r)) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (s - r))) is V11() real ext-real Element of REAL
a is ordinal natural V11() real ext-real non negative set
TOP-REAL a is non empty TopSpace-like V126() V191() V192() V209() V210() V211() V212() V213() V214() V215() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL a) is non empty set
b is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
r is V11() real ext-real non positive set
(a,b,r) is Element of K6( the carrier of (TOP-REAL a))
K6( the carrier of (TOP-REAL a)) is set
{ b1 where b1 is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a) : not r <= |.(b1 - b).| } is set
w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
w - b is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- b is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- b is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
- 1 is V11() real ext-real non positive set
(- 1) * b is V16() V21() set
K382((TOP-REAL a),w,(- b)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
the U7 of (TOP-REAL a) is V16() V21() V30(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) Element of K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)))
K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)) is V16() set
K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) is V16() set
K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a))) is set
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),w,(- b)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
w + (- b) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
w - b is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K448(b) is V16() V21() complex-yielding set
K419(w,K448(b)) is V16() V21() set
|.(w - b).| is V11() real ext-real non negative Element of REAL
sqr (w - b) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt ((w - b),(w - b)) is V16() V21() set
Sum (sqr (w - b)) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (w - b))) is V11() real ext-real Element of REAL
a is ordinal natural V11() real ext-real non negative set
TOP-REAL a is non empty TopSpace-like V126() V191() V192() V209() V210() V211() V212() V213() V214() V215() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL a) is non empty set
b is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
r is non empty V11() real ext-real positive non negative set
(a,b,r) is Element of K6( the carrier of (TOP-REAL a))
K6( the carrier of (TOP-REAL a)) is set
{ b1 where b1 is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a) : not r <= |.(b1 - b).| } is set
Euclid a is non empty strict Reflexive discerning V103() triangle MetrStruct
REAL a is non empty V24() FinSequence-membered FinSequenceSet of REAL
a -tuples_on REAL is V24() FinSequence-membered FinSequenceSet of REAL
Pitag_dist a is V16() V21() V30(K7((REAL a),(REAL a)), REAL ) complex-yielding ext-real-valued real-valued Element of K6(K7(K7((REAL a),(REAL a)),REAL))
K7((REAL a),(REAL a)) is V16() set
K7(K7((REAL a),(REAL a)),REAL) is V16() complex-yielding ext-real-valued real-valued set
K6(K7(K7((REAL a),(REAL a)),REAL)) is set
MetrStruct(# (REAL a),(Pitag_dist a) #) is strict MetrStruct
the carrier of (Euclid a) is non empty set
w is Element of the carrier of (Euclid a)
Ball (w,r) is bounded Element of K6( the carrier of (Euclid a))
K6( the carrier of (Euclid a)) is set
a is ordinal natural V11() real ext-real non negative V33() V34() V179() V180() V181() V182() V183() V184() Element of NAT
TOP-REAL a is non empty TopSpace-like V126() V191() V192() V209() V210() V211() V212() V213() V214() V215() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL a) is non empty set
r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
b is V11() real ext-real set
(a,r,b) is Element of K6( the carrier of (TOP-REAL a))
K6( the carrier of (TOP-REAL a)) is set
{ b1 where b1 is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a) : not b <= |.(b1 - r).| } is set
a is ordinal natural V11() real ext-real non negative V33() V34() V179() V180() V181() V182() V183() V184() Element of NAT
TOP-REAL a is non empty TopSpace-like V126() V191() V192() V209() V210() V211() V212() V213() V214() V215() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL a) is non empty set
r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
b is V11() real ext-real set
(a,r,b) is Element of K6( the carrier of (TOP-REAL a))
K6( the carrier of (TOP-REAL a)) is set
{ b1 where b1 is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a) : not b <= |.(b1 - r).| } is set
a is ordinal natural V11() real ext-real non negative set
TOP-REAL a is non empty TopSpace-like V126() V191() V192() V209() V210() V211() V212() V213() V214() V215() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL a) is non empty set
b is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
r is non empty V11() real ext-real non positive negative set
(a,b,r) is Element of K6( the carrier of (TOP-REAL a))
K6( the carrier of (TOP-REAL a)) is set
{ b1 where b1 is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a) : |.(b1 - b).| <= r } is set
w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
w - b is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- b is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- b is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
- 1 is V11() real ext-real non positive set
(- 1) * b is V16() V21() set
K382((TOP-REAL a),w,(- b)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
the U7 of (TOP-REAL a) is V16() V21() V30(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) Element of K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)))
K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)) is V16() set
K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) is V16() set
K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a))) is set
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),w,(- b)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
w + (- b) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
w - b is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K448(b) is V16() V21() complex-yielding set
K419(w,K448(b)) is V16() V21() set
|.(w - b).| is V11() real ext-real non negative Element of REAL
sqr (w - b) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt ((w - b),(w - b)) is V16() V21() set
Sum (sqr (w - b)) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (w - b))) is V11() real ext-real Element of REAL
a is ordinal natural V11() real ext-real non negative set
TOP-REAL a is non empty TopSpace-like V126() V191() V192() V209() V210() V211() V212() V213() V214() V215() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL a) is non empty set
b is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
r is V11() real ext-real non negative set
(a,b,r) is Element of K6( the carrier of (TOP-REAL a))
K6( the carrier of (TOP-REAL a)) is set
{ b1 where b1 is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a) : |.(b1 - b).| <= r } is set
b - b is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- b is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- b is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
- 1 is V11() real ext-real non positive set
(- 1) * b is V16() V21() set
K382((TOP-REAL a),b,(- b)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
the U7 of (TOP-REAL a) is V16() V21() V30(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) Element of K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)))
K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)) is V16() set
K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) is V16() set
K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a))) is set
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),b,(- b)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
b + (- b) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
b - b is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K448(b) is V16() V21() complex-yielding set
K419(b,K448(b)) is V16() V21() set
|.(b - b).| is V11() real ext-real non negative Element of REAL
sqr (b - b) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt ((b - b),(b - b)) is V16() V21() set
Sum (sqr (b - b)) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (b - b))) is V11() real ext-real Element of REAL
a is ordinal natural V11() real ext-real non negative V33() V34() V179() V180() V181() V182() V183() V184() Element of NAT
TOP-REAL a is non empty TopSpace-like V126() V191() V192() V209() V210() V211() V212() V213() V214() V215() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL a) is non empty set
r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
b is V11() real ext-real set
(a,r,b) is Element of K6( the carrier of (TOP-REAL a))
K6( the carrier of (TOP-REAL a)) is set
{ b1 where b1 is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a) : |.(b1 - r).| <= b } is set
a is ordinal natural V11() real ext-real non negative V33() V34() V179() V180() V181() V182() V183() V184() Element of NAT
TOP-REAL a is non empty TopSpace-like V126() V191() V192() V209() V210() V211() V212() V213() V214() V215() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL a) is non empty set
r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
b is V11() real ext-real set
(a,r,b) is Element of K6( the carrier of (TOP-REAL a))
K6( the carrier of (TOP-REAL a)) is set
{ b1 where b1 is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a) : |.(b1 - r).| <= b } is set
a is ordinal natural V11() real ext-real non negative V33() V34() V179() V180() V181() V182() V183() V184() Element of NAT
TOP-REAL a is non empty TopSpace-like V126() V191() V192() V209() V210() V211() V212() V213() V214() V215() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL a) is non empty set
b is V11() real ext-real set
abs b is V11() real ext-real Element of REAL
r is V11() real ext-real set
b + r is V11() real ext-real set
abs r is V11() real ext-real Element of REAL
(abs b) + (abs r) is V11() real ext-real Element of REAL
w is V11() real ext-real set
s is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
b * s is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
b * s is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
t is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(a,t,w) is Element of K6( the carrier of (TOP-REAL a))
K6( the carrier of (TOP-REAL a)) is set
{ b1 where b1 is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a) : |.(b1 - t).| <= w } is set
(a,t,w) is Element of K6( the carrier of (TOP-REAL a))
{ b1 where b1 is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a) : not w <= |.(b1 - t).| } is set
G is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
r * G is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
r * G is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(b * s) + (r * G) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
the U7 of (TOP-REAL a) is V16() V21() V30(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) Element of K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)))
K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)) is V16() set
K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) is V16() set
K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a))) is set
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(b * s),(r * G)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(b * s) + (r * G) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
G - t is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- t is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- t is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
- 1 is V11() real ext-real non positive set
(- 1) * t is V16() V21() set
K382((TOP-REAL a),G,(- t)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),G,(- t)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
G + (- t) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
G - t is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K448(t) is V16() V21() complex-yielding set
K419(G,K448(t)) is V16() V21() set
|.(G - t).| is V11() real ext-real non negative Element of REAL
sqr (G - t) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt ((G - t),(G - t)) is V16() V21() set
Sum (sqr (G - t)) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (G - t))) is V11() real ext-real Element of REAL
t - G is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- G is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- G is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(- 1) * G is V16() V21() set
K382((TOP-REAL a),t,(- G)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),t,(- G)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
t + (- G) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
t - G is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K448(G) is V16() V21() complex-yielding set
K419(t,K448(G)) is V16() V21() set
|.(t - G).| is V11() real ext-real non negative Element of REAL
sqr (t - G) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt ((t - G),(t - G)) is V16() V21() set
Sum (sqr (t - G)) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (t - G))) is V11() real ext-real Element of REAL
s - t is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K382((TOP-REAL a),s,(- t)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),s,(- t)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
s + (- t) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
s - t is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K419(s,K448(t)) is V16() V21() set
|.(s - t).| is V11() real ext-real non negative Element of REAL
sqr (s - t) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt ((s - t),(s - t)) is V16() V21() set
Sum (sqr (s - t)) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (s - t))) is V11() real ext-real Element of REAL
t - s is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- s is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- s is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(- 1) * s is V16() V21() set
K382((TOP-REAL a),t,(- s)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),t,(- s)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
t + (- s) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
t - s is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K448(s) is V16() V21() complex-yielding set
K419(t,K448(s)) is V16() V21() set
|.(t - s).| is V11() real ext-real non negative Element of REAL
sqr (t - s) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt ((t - s),(t - s)) is V16() V21() set
Sum (sqr (t - s)) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (t - s))) is V11() real ext-real Element of REAL
(abs b) * |.(t - s).| is V11() real ext-real Element of REAL
(abs b) * w is V11() real ext-real Element of REAL
(abs r) * w is V11() real ext-real Element of REAL
(abs r) * |.(t - G).| is V11() real ext-real Element of REAL
((abs b) * w) + ((abs r) * w) is V11() real ext-real Element of REAL
((abs b) * |.(t - s).|) + ((abs r) * |.(t - G).|) is V11() real ext-real Element of REAL
((abs b) + (abs r)) * w is V11() real ext-real Element of REAL
1 * w is V11() real ext-real Element of REAL
b * (t - s) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
b * (t - s) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
|.(b * (t - s)).| is V11() real ext-real non negative Element of REAL
sqr (b * (t - s)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt ((b * (t - s)),(b * (t - s))) is V16() V21() set
Sum (sqr (b * (t - s))) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (b * (t - s)))) is V11() real ext-real Element of REAL
|.(b * (t - s)).| + ((abs r) * |.(t - G).|) is V11() real ext-real Element of REAL
r * (t - G) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
r * (t - G) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
|.(r * (t - G)).| is V11() real ext-real non negative Element of REAL
sqr (r * (t - G)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt ((r * (t - G)),(r * (t - G))) is V16() V21() set
Sum (sqr (r * (t - G))) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (r * (t - G)))) is V11() real ext-real Element of REAL
|.(b * (t - s)).| + |.(r * (t - G)).| is V11() real ext-real non negative Element of REAL
b * t is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
b * t is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
r * t is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
r * t is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(b * t) + (r * t) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(b * t),(r * t)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(b * t) + (r * t) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((b * t) + (r * t)) - ((b * s) + (r * G)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- ((b * s) + (r * G)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- ((b * s) + (r * G)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(- 1) * ((b * s) + (r * G)) is V16() V21() set
K382((TOP-REAL a),((b * t) + (r * t)),(- ((b * s) + (r * G)))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((b * t) + (r * t)),(- ((b * s) + (r * G)))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((b * t) + (r * t)) + (- ((b * s) + (r * G))) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((b * t) + (r * t)) - ((b * s) + (r * G)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K448(((b * s) + (r * G))) is V16() V21() complex-yielding set
K419(((b * t) + (r * t)),K448(((b * s) + (r * G)))) is V16() V21() set
|.(((b * t) + (r * t)) - ((b * s) + (r * G))).| is V11() real ext-real non negative Element of REAL
sqr (((b * t) + (r * t)) - ((b * s) + (r * G))) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt ((((b * t) + (r * t)) - ((b * s) + (r * G))),(((b * t) + (r * t)) - ((b * s) + (r * G)))) is V16() V21() set
Sum (sqr (((b * t) + (r * t)) - ((b * s) + (r * G)))) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (((b * t) + (r * t)) - ((b * s) + (r * G))))) is V11() real ext-real Element of REAL
(b * t) - ((b * s) + (r * G)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K382((TOP-REAL a),(b * t),(- ((b * s) + (r * G)))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(b * t),(- ((b * s) + (r * G)))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(b * t) + (- ((b * s) + (r * G))) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(b * t) - ((b * s) + (r * G)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K419((b * t),K448(((b * s) + (r * G)))) is V16() V21() set
((b * t) - ((b * s) + (r * G))) + (r * t) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((b * t) - ((b * s) + (r * G))),(r * t)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((b * t) - ((b * s) + (r * G))) + (r * t) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
|.(((b * t) - ((b * s) + (r * G))) + (r * t)).| is V11() real ext-real non negative Element of REAL
sqr (((b * t) - ((b * s) + (r * G))) + (r * t)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt ((((b * t) - ((b * s) + (r * G))) + (r * t)),(((b * t) - ((b * s) + (r * G))) + (r * t))) is V16() V21() set
Sum (sqr (((b * t) - ((b * s) + (r * G))) + (r * t))) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (((b * t) - ((b * s) + (r * G))) + (r * t)))) is V11() real ext-real Element of REAL
(b * t) - (b * s) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- (b * s) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- (b * s) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(- 1) * (b * s) is V16() V21() set
K382((TOP-REAL a),(b * t),(- (b * s))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(b * t),(- (b * s))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(b * t) + (- (b * s)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(b * t) - (b * s) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K448((b * s)) is V16() V21() complex-yielding set
K419((b * t),K448((b * s))) is V16() V21() set
((b * t) - (b * s)) - (r * G) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- (r * G) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- (r * G) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(- 1) * (r * G) is V16() V21() set
K382((TOP-REAL a),((b * t) - (b * s)),(- (r * G))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((b * t) - (b * s)),(- (r * G))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((b * t) - (b * s)) + (- (r * G)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((b * t) - (b * s)) - (r * G) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K448((r * G)) is V16() V21() complex-yielding set
K419(((b * t) - (b * s)),K448((r * G))) is V16() V21() set
(((b * t) - (b * s)) - (r * G)) + (r * t) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(((b * t) - (b * s)) - (r * G)),(r * t)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(((b * t) - (b * s)) - (r * G)) + (r * t) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
|.((((b * t) - (b * s)) - (r * G)) + (r * t)).| is V11() real ext-real non negative Element of REAL
sqr ((((b * t) - (b * s)) - (r * G)) + (r * t)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt (((((b * t) - (b * s)) - (r * G)) + (r * t)),((((b * t) - (b * s)) - (r * G)) + (r * t))) is V16() V21() set
Sum (sqr ((((b * t) - (b * s)) - (r * G)) + (r * t))) is V11() real ext-real Element of REAL
sqrt (Sum (sqr ((((b * t) - (b * s)) - (r * G)) + (r * t)))) is V11() real ext-real Element of REAL
((b * t) - (b * s)) + (r * t) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((b * t) - (b * s)),(r * t)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((b * t) - (b * s)) + (r * t) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((b * t) - (b * s)) + (r * t)) - (r * G) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K382((TOP-REAL a),(((b * t) - (b * s)) + (r * t)),(- (r * G))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(((b * t) - (b * s)) + (r * t)),(- (r * G))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(((b * t) - (b * s)) + (r * t)) + (- (r * G)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((b * t) - (b * s)) + (r * t)) - (r * G) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K419((((b * t) - (b * s)) + (r * t)),K448((r * G))) is V16() V21() set
|.((((b * t) - (b * s)) + (r * t)) - (r * G)).| is V11() real ext-real non negative Element of REAL
sqr ((((b * t) - (b * s)) + (r * t)) - (r * G)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt (((((b * t) - (b * s)) + (r * t)) - (r * G)),((((b * t) - (b * s)) + (r * t)) - (r * G))) is V16() V21() set
Sum (sqr ((((b * t) - (b * s)) + (r * t)) - (r * G))) is V11() real ext-real Element of REAL
sqrt (Sum (sqr ((((b * t) - (b * s)) + (r * t)) - (r * G)))) is V11() real ext-real Element of REAL
(r * t) - (r * G) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K382((TOP-REAL a),(r * t),(- (r * G))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(r * t),(- (r * G))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(r * t) + (- (r * G)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(r * t) - (r * G) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K419((r * t),K448((r * G))) is V16() V21() set
((b * t) - (b * s)) + ((r * t) - (r * G)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((b * t) - (b * s)),((r * t) - (r * G))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((b * t) - (b * s)) + ((r * t) - (r * G)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
|.(((b * t) - (b * s)) + ((r * t) - (r * G))).| is V11() real ext-real non negative Element of REAL
sqr (((b * t) - (b * s)) + ((r * t) - (r * G))) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt ((((b * t) - (b * s)) + ((r * t) - (r * G))),(((b * t) - (b * s)) + ((r * t) - (r * G)))) is V16() V21() set
Sum (sqr (((b * t) - (b * s)) + ((r * t) - (r * G)))) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (((b * t) - (b * s)) + ((r * t) - (r * G))))) is V11() real ext-real Element of REAL
(b * (t - s)) + ((r * t) - (r * G)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(b * (t - s)),((r * t) - (r * G))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(b * (t - s)) + ((r * t) - (r * G)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
|.((b * (t - s)) + ((r * t) - (r * G))).| is V11() real ext-real non negative Element of REAL
sqr ((b * (t - s)) + ((r * t) - (r * G))) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt (((b * (t - s)) + ((r * t) - (r * G))),((b * (t - s)) + ((r * t) - (r * G)))) is V16() V21() set
Sum (sqr ((b * (t - s)) + ((r * t) - (r * G)))) is V11() real ext-real Element of REAL
sqrt (Sum (sqr ((b * (t - s)) + ((r * t) - (r * G))))) is V11() real ext-real Element of REAL
(b * (t - s)) + (r * (t - G)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(b * (t - s)),(r * (t - G))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(b * (t - s)) + (r * (t - G)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
|.((b * (t - s)) + (r * (t - G))).| is V11() real ext-real non negative Element of REAL
sqr ((b * (t - s)) + (r * (t - G))) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt (((b * (t - s)) + (r * (t - G))),((b * (t - s)) + (r * (t - G)))) is V16() V21() set
Sum (sqr ((b * (t - s)) + (r * (t - G)))) is V11() real ext-real Element of REAL
sqrt (Sum (sqr ((b * (t - s)) + (r * (t - G))))) is V11() real ext-real Element of REAL
((b * s) + (r * G)) - ((b * t) + (r * t)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- ((b * t) + (r * t)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- ((b * t) + (r * t)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(- 1) * ((b * t) + (r * t)) is V16() V21() set
K382((TOP-REAL a),((b * s) + (r * G)),(- ((b * t) + (r * t)))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((b * s) + (r * G)),(- ((b * t) + (r * t)))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((b * s) + (r * G)) + (- ((b * t) + (r * t))) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((b * s) + (r * G)) - ((b * t) + (r * t)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K448(((b * t) + (r * t))) is V16() V21() complex-yielding set
K419(((b * s) + (r * G)),K448(((b * t) + (r * t)))) is V16() V21() set
|.(((b * s) + (r * G)) - ((b * t) + (r * t))).| is V11() real ext-real non negative Element of REAL
sqr (((b * s) + (r * G)) - ((b * t) + (r * t))) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt ((((b * s) + (r * G)) - ((b * t) + (r * t))),(((b * s) + (r * G)) - ((b * t) + (r * t)))) is V16() V21() set
Sum (sqr (((b * s) + (r * G)) - ((b * t) + (r * t)))) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (((b * s) + (r * G)) - ((b * t) + (r * t))))) is V11() real ext-real Element of REAL
(b + r) * t is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(b + r) * t is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
a is ordinal natural V11() real ext-real non negative set
TOP-REAL a is non empty TopSpace-like V126() V191() V192() V209() V210() V211() V212() V213() V214() V215() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL a) is non empty set
b is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
r is V11() real ext-real set
(a,b,r) is Element of K6( the carrier of (TOP-REAL a))
K6( the carrier of (TOP-REAL a)) is set
{ b1 where b1 is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a) : not r <= |.(b1 - b).| } is set
Euclid a is non empty strict Reflexive discerning V103() triangle MetrStruct
REAL a is non empty V24() FinSequence-membered FinSequenceSet of REAL
a -tuples_on REAL is V24() FinSequence-membered FinSequenceSet of REAL
Pitag_dist a is V16() V21() V30(K7((REAL a),(REAL a)), REAL ) complex-yielding ext-real-valued real-valued Element of K6(K7(K7((REAL a),(REAL a)),REAL))
K7((REAL a),(REAL a)) is V16() set
K7(K7((REAL a),(REAL a)),REAL) is V16() complex-yielding ext-real-valued real-valued set
K6(K7(K7((REAL a),(REAL a)),REAL)) is set
MetrStruct(# (REAL a),(Pitag_dist a) #) is strict MetrStruct
the carrier of (Euclid a) is non empty set
w is Element of the carrier of (Euclid a)
Ball (w,r) is bounded Element of K6( the carrier of (Euclid a))
K6( the carrier of (Euclid a)) is set
(a,b,r) is Element of K6( the carrier of (TOP-REAL a))
{ b1 where b1 is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a) : |.(b1 - b).| <= r } is set
Euclid a is non empty strict Reflexive discerning V103() triangle MetrStruct
REAL a is non empty V24() FinSequence-membered FinSequenceSet of REAL
a -tuples_on REAL is V24() FinSequence-membered FinSequenceSet of REAL
Pitag_dist a is V16() V21() V30(K7((REAL a),(REAL a)), REAL ) complex-yielding ext-real-valued real-valued Element of K6(K7(K7((REAL a),(REAL a)),REAL))
K7((REAL a),(REAL a)) is V16() set
K7(K7((REAL a),(REAL a)),REAL) is V16() complex-yielding ext-real-valued real-valued set
K6(K7(K7((REAL a),(REAL a)),REAL)) is set
MetrStruct(# (REAL a),(Pitag_dist a) #) is strict MetrStruct
the carrier of (Euclid a) is non empty set
w is Element of the carrier of (Euclid a)
cl_Ball (w,r) is Element of K6( the carrier of (Euclid a))
K6( the carrier of (Euclid a)) is set
(a,b,r) is Element of K6( the carrier of (TOP-REAL a))
{ b1 where b1 is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a) : |.(b1 - b).| = r } is set
Euclid a is non empty strict Reflexive discerning V103() triangle MetrStruct
REAL a is non empty V24() FinSequence-membered FinSequenceSet of REAL
a -tuples_on REAL is V24() FinSequence-membered FinSequenceSet of REAL
Pitag_dist a is V16() V21() V30(K7((REAL a),(REAL a)), REAL ) complex-yielding ext-real-valued real-valued Element of K6(K7(K7((REAL a),(REAL a)),REAL))
K7((REAL a),(REAL a)) is V16() set
K7(K7((REAL a),(REAL a)),REAL) is V16() complex-yielding ext-real-valued real-valued set
K6(K7(K7((REAL a),(REAL a)),REAL)) is set
MetrStruct(# (REAL a),(Pitag_dist a) #) is strict MetrStruct
the carrier of (Euclid a) is non empty set
w is Element of the carrier of (Euclid a)
Sphere (w,r) is Element of K6( the carrier of (Euclid a))
K6( the carrier of (Euclid a)) is set
a is ordinal natural V11() real ext-real non negative V33() V34() V179() V180() V181() V182() V183() V184() Element of NAT
TOP-REAL a is non empty TopSpace-like V126() V191() V192() V209() V210() V211() V212() V213() V214() V215() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL a) is non empty set
b is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
r is V11() real ext-real set
(a,b,r) is open Element of K6( the carrier of (TOP-REAL a))
K6( the carrier of (TOP-REAL a)) is set
{ b1 where b1 is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a) : not r <= |.(b1 - b).| } is set
Euclid a is non empty strict Reflexive discerning V103() triangle MetrStruct
REAL a is non empty V24() FinSequence-membered FinSequenceSet of REAL
a -tuples_on REAL is V24() FinSequence-membered FinSequenceSet of REAL
Pitag_dist a is V16() V21() V30(K7((REAL a),(REAL a)), REAL ) complex-yielding ext-real-valued real-valued Element of K6(K7(K7((REAL a),(REAL a)),REAL))
K7((REAL a),(REAL a)) is V16() set
K7(K7((REAL a),(REAL a)),REAL) is V16() complex-yielding ext-real-valued real-valued set
K6(K7(K7((REAL a),(REAL a)),REAL)) is set
MetrStruct(# (REAL a),(Pitag_dist a) #) is strict MetrStruct
the carrier of (Euclid a) is non empty set
w is Element of the carrier of (Euclid a)
Ball (w,r) is bounded Element of K6( the carrier of (Euclid a))
K6( the carrier of (Euclid a)) is set
(a,b,r) is closed Element of K6( the carrier of (TOP-REAL a))
{ b1 where b1 is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a) : |.(b1 - b).| <= r } is set
Euclid a is non empty strict Reflexive discerning V103() triangle MetrStruct
REAL a is non empty V24() FinSequence-membered FinSequenceSet of REAL
a -tuples_on REAL is V24() FinSequence-membered FinSequenceSet of REAL
Pitag_dist a is V16() V21() V30(K7((REAL a),(REAL a)), REAL ) complex-yielding ext-real-valued real-valued Element of K6(K7(K7((REAL a),(REAL a)),REAL))
K7((REAL a),(REAL a)) is V16() set
K7(K7((REAL a),(REAL a)),REAL) is V16() complex-yielding ext-real-valued real-valued set
K6(K7(K7((REAL a),(REAL a)),REAL)) is set
MetrStruct(# (REAL a),(Pitag_dist a) #) is strict MetrStruct
the carrier of (Euclid a) is non empty set
w is Element of the carrier of (Euclid a)
cl_Ball (w,r) is Element of K6( the carrier of (Euclid a))
K6( the carrier of (Euclid a)) is set
(a,b,r) is closed Element of K6( the carrier of (TOP-REAL a))
{ b1 where b1 is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a) : |.(b1 - b).| = r } is set
Euclid a is non empty strict Reflexive discerning V103() triangle MetrStruct
REAL a is non empty V24() FinSequence-membered FinSequenceSet of REAL
a -tuples_on REAL is V24() FinSequence-membered FinSequenceSet of REAL
Pitag_dist a is V16() V21() V30(K7((REAL a),(REAL a)), REAL ) complex-yielding ext-real-valued real-valued Element of K6(K7(K7((REAL a),(REAL a)),REAL))
K7((REAL a),(REAL a)) is V16() set
K7(K7((REAL a),(REAL a)),REAL) is V16() complex-yielding ext-real-valued real-valued set
K6(K7(K7((REAL a),(REAL a)),REAL)) is set
MetrStruct(# (REAL a),(Pitag_dist a) #) is strict MetrStruct
the carrier of (Euclid a) is non empty set
w is Element of the carrier of (Euclid a)
Sphere (w,r) is Element of K6( the carrier of (Euclid a))
K6( the carrier of (Euclid a)) is set
a is ordinal natural V11() real ext-real non negative V33() V34() V179() V180() V181() V182() V183() V184() Element of NAT
TOP-REAL a is non empty TopSpace-like V126() V191() V192() V209() V210() V211() V212() V213() V214() V215() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL a) is non empty set
K6( the carrier of (TOP-REAL a)) is set
b is V11() real ext-real set
r is Element of K6( the carrier of (TOP-REAL a))
w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
{ b1 where b1 is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a) : |.(b1 - w).| <= b } is set
s is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
t is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
LSeg (s,t) is Element of K6( the carrier of (TOP-REAL a))
{ (((1 - b1) * s) + (b1 * t)) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
G is set
S is V11() real ext-real Element of REAL
1 - S is V11() real ext-real Element of REAL
- S is V11() real ext-real set
1 + (- S) is V11() real ext-real set
(1 - S) * s is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(1 - S) * s is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
S * t is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
S * t is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - S) * s) + (S * t) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
the U7 of (TOP-REAL a) is V16() V21() V30(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) Element of K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)))
K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)) is V16() set
K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) is V16() set
K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a))) is set
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 - S) * s),(S * t)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - S) * s) + (S * t) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
abs S is V11() real ext-real Element of REAL
s - w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
- 1 is V11() real ext-real non positive set
(- 1) * w is V16() V21() set
K382((TOP-REAL a),s,(- w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),s,(- w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
s + (- w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
s - w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K448(w) is V16() V21() complex-yielding set
K419(s,K448(w)) is V16() V21() set
(1 - S) * (s - w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(1 - S) * (s - w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
|.((1 - S) * (s - w)).| is V11() real ext-real non negative Element of REAL
sqr ((1 - S) * (s - w)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt (((1 - S) * (s - w)),((1 - S) * (s - w))) is V16() V21() set
Sum (sqr ((1 - S) * (s - w))) is V11() real ext-real Element of REAL
sqrt (Sum (sqr ((1 - S) * (s - w)))) is V11() real ext-real Element of REAL
abs (1 - S) is V11() real ext-real Element of REAL
|.(s - w).| is V11() real ext-real non negative Element of REAL
sqr (s - w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt ((s - w),(s - w)) is V16() V21() set
Sum (sqr (s - w)) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (s - w))) is V11() real ext-real Element of REAL
(abs (1 - S)) * |.(s - w).| is V11() real ext-real Element of REAL
t - w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K382((TOP-REAL a),t,(- w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),t,(- w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
t + (- w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
t - w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K419(t,K448(w)) is V16() V21() set
S * (t - w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
S * (t - w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
|.(S * (t - w)).| is V11() real ext-real non negative Element of REAL
sqr (S * (t - w)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt ((S * (t - w)),(S * (t - w))) is V16() V21() set
Sum (sqr (S * (t - w))) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (S * (t - w)))) is V11() real ext-real Element of REAL
|.(t - w).| is V11() real ext-real non negative Element of REAL
sqr (t - w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt ((t - w),(t - w)) is V16() V21() set
Sum (sqr (t - w)) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (t - w))) is V11() real ext-real Element of REAL
(abs S) * |.(t - w).| is V11() real ext-real Element of REAL
(abs S) * b is V11() real ext-real Element of REAL
Y is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
Y - w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K382((TOP-REAL a),Y,(- w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),Y,(- w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
Y + (- w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
Y - w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K419(Y,K448(w)) is V16() V21() set
|.(Y - w).| is V11() real ext-real non negative Element of REAL
sqr (Y - w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt ((Y - w),(Y - w)) is V16() V21() set
Sum (sqr (Y - w)) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (Y - w))) is V11() real ext-real Element of REAL
(1 - S) * w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(1 - S) * w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
S * w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
S * w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - S) * w) + (S * w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 - S) * w),(S * w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - S) * w) + (S * w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
1 * w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
1 * w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(1 * w) - (S * w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- (S * w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- (S * w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(- 1) * (S * w) is V16() V21() set
K382((TOP-REAL a),(1 * w),(- (S * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(1 * w),(- (S * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(1 * w) + (- (S * w)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(1 * w) - (S * w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K448((S * w)) is V16() V21() complex-yielding set
K419((1 * w),K448((S * w))) is V16() V21() set
((1 * w) - (S * w)) + (S * w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 * w) - (S * w)),(S * w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 * w) - (S * w)) + (S * w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
T is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
T - w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K382((TOP-REAL a),T,(- w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),T,(- w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
T + (- w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
T - w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K419(T,K448(w)) is V16() V21() set
(((1 - S) * s) + (S * t)) - ((1 - S) * w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- ((1 - S) * w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- ((1 - S) * w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(- 1) * ((1 - S) * w) is V16() V21() set
K382((TOP-REAL a),(((1 - S) * s) + (S * t)),(- ((1 - S) * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(((1 - S) * s) + (S * t)),(- ((1 - S) * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(((1 - S) * s) + (S * t)) + (- ((1 - S) * w)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((1 - S) * s) + (S * t)) - ((1 - S) * w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K448(((1 - S) * w)) is V16() V21() complex-yielding set
K419((((1 - S) * s) + (S * t)),K448(((1 - S) * w))) is V16() V21() set
((((1 - S) * s) + (S * t)) - ((1 - S) * w)) - (S * w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K382((TOP-REAL a),((((1 - S) * s) + (S * t)) - ((1 - S) * w)),(- (S * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((((1 - S) * s) + (S * t)) - ((1 - S) * w)),(- (S * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((((1 - S) * s) + (S * t)) - ((1 - S) * w)) + (- (S * w)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((((1 - S) * s) + (S * t)) - ((1 - S) * w)) - (S * w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K419(((((1 - S) * s) + (S * t)) - ((1 - S) * w)),K448((S * w))) is V16() V21() set
((1 - S) * s) - ((1 - S) * w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K382((TOP-REAL a),((1 - S) * s),(- ((1 - S) * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 - S) * s),(- ((1 - S) * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - S) * s) + (- ((1 - S) * w)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - S) * s) - ((1 - S) * w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K419(((1 - S) * s),K448(((1 - S) * w))) is V16() V21() set
(((1 - S) * s) - ((1 - S) * w)) + (S * t) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(((1 - S) * s) - ((1 - S) * w)),(S * t)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(((1 - S) * s) - ((1 - S) * w)) + (S * t) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((((1 - S) * s) - ((1 - S) * w)) + (S * t)) - (S * w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K382((TOP-REAL a),((((1 - S) * s) - ((1 - S) * w)) + (S * t)),(- (S * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((((1 - S) * s) - ((1 - S) * w)) + (S * t)),(- (S * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((((1 - S) * s) - ((1 - S) * w)) + (S * t)) + (- (S * w)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((((1 - S) * s) - ((1 - S) * w)) + (S * t)) - (S * w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K419(((((1 - S) * s) - ((1 - S) * w)) + (S * t)),K448((S * w))) is V16() V21() set
((1 - S) * (s - w)) + (S * t) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 - S) * (s - w)),(S * t)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - S) * (s - w)) + (S * t) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((1 - S) * (s - w)) + (S * t)) - (S * w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K382((TOP-REAL a),(((1 - S) * (s - w)) + (S * t)),(- (S * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(((1 - S) * (s - w)) + (S * t)),(- (S * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(((1 - S) * (s - w)) + (S * t)) + (- (S * w)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((1 - S) * (s - w)) + (S * t)) - (S * w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K419((((1 - S) * (s - w)) + (S * t)),K448((S * w))) is V16() V21() set
(S * t) - (S * w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K382((TOP-REAL a),(S * t),(- (S * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(S * t),(- (S * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(S * t) + (- (S * w)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(S * t) - (S * w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K419((S * t),K448((S * w))) is V16() V21() set
((1 - S) * (s - w)) + ((S * t) - (S * w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 - S) * (s - w)),((S * t) - (S * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - S) * (s - w)) + ((S * t) - (S * w)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - S) * (s - w)) + (S * (t - w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 - S) * (s - w)),(S * (t - w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - S) * (s - w)) + (S * (t - w)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
|.(T - w).| is V11() real ext-real non negative Element of REAL
sqr (T - w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt ((T - w),(T - w)) is V16() V21() set
Sum (sqr (T - w)) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (T - w))) is V11() real ext-real Element of REAL
|.((1 - S) * (s - w)).| + |.(S * (t - w)).| is V11() real ext-real non negative Element of REAL
(abs (1 - S)) * b is V11() real ext-real Element of REAL
Y is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
Y - w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K382((TOP-REAL a),Y,(- w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),Y,(- w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
Y + (- w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
Y - w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K419(Y,K448(w)) is V16() V21() set
|.(Y - w).| is V11() real ext-real non negative Element of REAL
sqr (Y - w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt ((Y - w),(Y - w)) is V16() V21() set
Sum (sqr (Y - w)) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (Y - w))) is V11() real ext-real Element of REAL
(1 - S) * b is V11() real ext-real Element of REAL
S * b is V11() real ext-real Element of REAL
((1 - S) * b) + (S * b) is V11() real ext-real Element of REAL
(1 - S) + S is V11() real ext-real Element of REAL
0 + S is V11() real ext-real Element of REAL
a is ordinal natural V11() real ext-real non negative V33() V34() V179() V180() V181() V182() V183() V184() Element of NAT
TOP-REAL a is non empty TopSpace-like V126() V191() V192() V209() V210() V211() V212() V213() V214() V215() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL a) is non empty set
K6( the carrier of (TOP-REAL a)) is set
b is V11() real ext-real set
r is Element of K6( the carrier of (TOP-REAL a))
w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
{ b1 where b1 is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a) : not b <= |.(b1 - w).| } is set
Euclid a is non empty strict Reflexive discerning V103() triangle MetrStruct
REAL a is non empty V24() FinSequence-membered FinSequenceSet of REAL
a -tuples_on REAL is V24() FinSequence-membered FinSequenceSet of REAL
Pitag_dist a is V16() V21() V30(K7((REAL a),(REAL a)), REAL ) complex-yielding ext-real-valued real-valued Element of K6(K7(K7((REAL a),(REAL a)),REAL))
K7((REAL a),(REAL a)) is V16() set
K7(K7((REAL a),(REAL a)),REAL) is V16() complex-yielding ext-real-valued real-valued set
K6(K7(K7((REAL a),(REAL a)),REAL)) is set
MetrStruct(# (REAL a),(Pitag_dist a) #) is strict MetrStruct
the carrier of (Euclid a) is non empty set
t is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
G is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
LSeg (t,G) is Element of K6( the carrier of (TOP-REAL a))
{ (((1 - b1) * t) + (b1 * G)) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
s is Element of the carrier of (Euclid a)
Ball (s,b) is bounded Element of K6( the carrier of (Euclid a))
K6( the carrier of (Euclid a)) is set
(a,w,b) is open bounded Element of K6( the carrier of (TOP-REAL a))
a is ordinal natural V11() real ext-real non negative set
TOP-REAL a is non empty TopSpace-like V126() V191() V192() V209() V210() V211() V212() V213() V214() V215() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL a) is non empty set
b is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
r is V11() real ext-real set
(a,b,r) is open Element of K6( the carrier of (TOP-REAL a))
K6( the carrier of (TOP-REAL a)) is set
{ b1 where b1 is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a) : not r <= |.(b1 - b).| } is set
(a,b,r) is closed Element of K6( the carrier of (TOP-REAL a))
{ b1 where b1 is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a) : |.(b1 - b).| <= r } is set
a is ordinal natural V11() real ext-real non negative set
TOP-REAL a is non empty TopSpace-like V126() V191() V192() V209() V210() V211() V212() V213() V214() V215() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL a) is non empty set
K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)) is V16() set
K6(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a))) is set
a is ordinal natural V11() real ext-real non negative V33() V34() V179() V180() V181() V182() V183() V184() Element of NAT
TOP-REAL a is non empty TopSpace-like V126() V191() V192() V209() V210() V211() V212() V213() V214() V215() strict add-continuous Mult-continuous RLTopStruct
0. (TOP-REAL a) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like V69( TOP-REAL a) complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
the carrier of (TOP-REAL a) is non empty set
the ZeroF of (TOP-REAL a) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(TOP-REAL a) --> (0. (TOP-REAL a)) is V16() V21() V30( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)) continuous Element of K6(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)))
K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)) is V16() set
K6(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a))) is set
K208( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a),(0. (TOP-REAL a))) is V16() V21() V30( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)) Element of K6(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)))
r is V11() real ext-real set
w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
r * w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
r * w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((TOP-REAL a) --> (0. (TOP-REAL a))) . (r * w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((TOP-REAL a) --> (0. (TOP-REAL a))) . w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
r * (((TOP-REAL a) --> (0. (TOP-REAL a))) . w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
r * (((TOP-REAL a) --> (0. (TOP-REAL a))) . w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
r * (0. (TOP-REAL a)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
r * (0. (TOP-REAL a)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K382((TOP-REAL a),r,w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
the U7 of (TOP-REAL a) is V16() V21() V30(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) Element of K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)))
K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) is V16() set
K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a))) is set
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),r,w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
r + w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((TOP-REAL a) --> (0. (TOP-REAL a))) . K382((TOP-REAL a),r,w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((TOP-REAL a) --> (0. (TOP-REAL a))) . r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((TOP-REAL a) --> (0. (TOP-REAL a))) . w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K382((TOP-REAL a),(((TOP-REAL a) --> (0. (TOP-REAL a))) . r),(((TOP-REAL a) --> (0. (TOP-REAL a))) . w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(((TOP-REAL a) --> (0. (TOP-REAL a))) . r),(((TOP-REAL a) --> (0. (TOP-REAL a))) . w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(((TOP-REAL a) --> (0. (TOP-REAL a))) . r) + (((TOP-REAL a) --> (0. (TOP-REAL a))) . w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
r + w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((TOP-REAL a) --> (0. (TOP-REAL a))) . (r + w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(0. (TOP-REAL a)) + (0. (TOP-REAL a)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(0. (TOP-REAL a)),(0. (TOP-REAL a))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(0. (TOP-REAL a)) + (0. (TOP-REAL a)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((TOP-REAL a) --> (0. (TOP-REAL a))) . r) + (0. (TOP-REAL a)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(((TOP-REAL a) --> (0. (TOP-REAL a))) . r),(0. (TOP-REAL a))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(((TOP-REAL a) --> (0. (TOP-REAL a))) . r) + (0. (TOP-REAL a)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((TOP-REAL a) --> (0. (TOP-REAL a))) . r) + (((TOP-REAL a) --> (0. (TOP-REAL a))) . w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
a is ordinal natural V11() real ext-real non negative V33() V34() V179() V180() V181() V182() V183() V184() Element of NAT
TOP-REAL a is non empty TopSpace-like V126() V191() V192() V209() V210() V211() V212() V213() V214() V215() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL a) is non empty set
K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)) is V16() set
K6(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a))) is set
0. (TOP-REAL a) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like V69( TOP-REAL a) complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
the ZeroF of (TOP-REAL a) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(TOP-REAL a) --> (0. (TOP-REAL a)) is V16() V21() V30( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)) V30( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)) continuous continuous additive (a) Element of K6(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)))
K208( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a),(0. (TOP-REAL a))) is V16() V21() V30( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)) Element of K6(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)))
a is V11() real ext-real set
b is V11() real ext-real set
AffineMap (a,0,b,0) is V16() V21() V30( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)) Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
s is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
w is V11() real ext-real set
w * s is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
w * s is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(w * s) `1 is V11() real ext-real Element of REAL
s `1 is V11() real ext-real Element of REAL
w * (s `1) is V11() real ext-real Element of REAL
(w * s) `2 is V11() real ext-real Element of REAL
s `2 is V11() real ext-real Element of REAL
w * (s `2) is V11() real ext-real Element of REAL
(AffineMap (a,0,b,0)) . (w * s) is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
a * ((w * s) `1) is V11() real ext-real Element of REAL
(a * ((w * s) `1)) + 0 is V11() real ext-real Element of REAL
b * ((w * s) `2) is V11() real ext-real Element of REAL
(b * ((w * s) `2)) + 0 is V11() real ext-real Element of REAL
|[((a * ((w * s) `1)) + 0),((b * ((w * s) `2)) + 0)]| is non empty V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
a * (s `1) is V11() real ext-real Element of REAL
w * (a * (s `1)) is V11() real ext-real Element of REAL
b * (s `2) is V11() real ext-real Element of REAL
w * (b * (s `2)) is V11() real ext-real Element of REAL
|[(w * (a * (s `1))),(w * (b * (s `2)))]| is non empty V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(a * (s `1)) + 0 is V11() real ext-real Element of REAL
(b * (s `2)) + 0 is V11() real ext-real Element of REAL
|[((a * (s `1)) + 0),((b * (s `2)) + 0)]| is non empty V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
w * |[((a * (s `1)) + 0),((b * (s `2)) + 0)]| is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
w * |[((a * (s `1)) + 0),((b * (s `2)) + 0)]| is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(AffineMap (a,0,b,0)) . s is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
w * ((AffineMap (a,0,b,0)) . s) is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
w * ((AffineMap (a,0,b,0)) . s) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
w is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
s is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K382((TOP-REAL 2),w,s) is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) is V16() V21() V30(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2)) Element of K6(K7(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2)))
K7(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2)) is V16() set
K6(K7(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2))) is set
K350( the carrier of (TOP-REAL 2), the U7 of (TOP-REAL 2),w,s) is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
w + s is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(AffineMap (a,0,b,0)) . K382((TOP-REAL 2),w,s) is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(AffineMap (a,0,b,0)) . w is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(AffineMap (a,0,b,0)) . s is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K382((TOP-REAL 2),((AffineMap (a,0,b,0)) . w),((AffineMap (a,0,b,0)) . s)) is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K350( the carrier of (TOP-REAL 2), the U7 of (TOP-REAL 2),((AffineMap (a,0,b,0)) . w),((AffineMap (a,0,b,0)) . s)) is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((AffineMap (a,0,b,0)) . w) + ((AffineMap (a,0,b,0)) . s) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
w + s is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(w + s) `1 is V11() real ext-real Element of REAL
w `1 is V11() real ext-real Element of REAL
s `1 is V11() real ext-real Element of REAL
(w `1) + (s `1) is V11() real ext-real Element of REAL
(w + s) `2 is V11() real ext-real Element of REAL
w `2 is V11() real ext-real Element of REAL
s `2 is V11() real ext-real Element of REAL
(w `2) + (s `2) is V11() real ext-real Element of REAL
(AffineMap (a,0,b,0)) . (w + s) is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
a * ((w + s) `1) is V11() real ext-real Element of REAL
(a * ((w + s) `1)) + 0 is V11() real ext-real Element of REAL
b * ((w + s) `2) is V11() real ext-real Element of REAL
(b * ((w + s) `2)) + 0 is V11() real ext-real Element of REAL
|[((a * ((w + s) `1)) + 0),((b * ((w + s) `2)) + 0)]| is non empty V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
a * (w `1) is V11() real ext-real Element of REAL
a * (s `1) is V11() real ext-real Element of REAL
(a * (w `1)) + (a * (s `1)) is V11() real ext-real Element of REAL
b * (w `2) is V11() real ext-real Element of REAL
b * (s `2) is V11() real ext-real Element of REAL
(b * (w `2)) + (b * (s `2)) is V11() real ext-real Element of REAL
|[((a * (w `1)) + (a * (s `1))),((b * (w `2)) + (b * (s `2)))]| is non empty V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(a * (w `1)) + 0 is V11() real ext-real Element of REAL
(b * (w `2)) + 0 is V11() real ext-real Element of REAL
|[((a * (w `1)) + 0),((b * (w `2)) + 0)]| is non empty V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
|[(a * (s `1)),(b * (s `2))]| is non empty V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
|[((a * (w `1)) + 0),((b * (w `2)) + 0)]| + |[(a * (s `1)),(b * (s `2))]| is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K350( the carrier of (TOP-REAL 2), the U7 of (TOP-REAL 2),|[((a * (w `1)) + 0),((b * (w `2)) + 0)]|,|[(a * (s `1)),(b * (s `2))]|) is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
|[((a * (w `1)) + 0),((b * (w `2)) + 0)]| + |[(a * (s `1)),(b * (s `2))]| is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(a * (s `1)) + 0 is V11() real ext-real Element of REAL
(b * (s `2)) + 0 is V11() real ext-real Element of REAL
|[((a * (s `1)) + 0),((b * (s `2)) + 0)]| is non empty V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((AffineMap (a,0,b,0)) . w) + |[((a * (s `1)) + 0),((b * (s `2)) + 0)]| is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K350( the carrier of (TOP-REAL 2), the U7 of (TOP-REAL 2),((AffineMap (a,0,b,0)) . w),|[((a * (s `1)) + 0),((b * (s `2)) + 0)]|) is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((AffineMap (a,0,b,0)) . w) + |[((a * (s `1)) + 0),((b * (s `2)) + 0)]| is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((AffineMap (a,0,b,0)) . w) + ((AffineMap (a,0,b,0)) . s) is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
a is ordinal natural V11() real ext-real non negative V33() V34() V179() V180() V181() V182() V183() V184() Element of NAT
TOP-REAL a is non empty TopSpace-like V126() V191() V192() V209() V210() V211() V212() V213() V214() V215() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL a) is non empty set
K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)) is V16() set
K6(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a))) is set
K6( the carrier of (TOP-REAL a)) is set
b is V16() V21() V30( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)) additive (a) Element of K6(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)))
r is convex Element of K6( the carrier of (TOP-REAL a))
b .: r is Element of K6( the carrier of (TOP-REAL a))
w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
s is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
LSeg (w,s) is Element of K6( the carrier of (TOP-REAL a))
{ (((1 - b1) * w) + (b1 * s)) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
t is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
b . t is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
G is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
b . G is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
LSeg (t,G) is Element of K6( the carrier of (TOP-REAL a))
{ (((1 - b1) * t) + (b1 * G)) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
S is set
T is V11() real ext-real Element of REAL
1 - T is V11() real ext-real Element of REAL
- T is V11() real ext-real set
1 + (- T) is V11() real ext-real set
(1 - T) * w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(1 - T) * w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
T * s is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
T * s is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - T) * w) + (T * s) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
the U7 of (TOP-REAL a) is V16() V21() V30(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) Element of K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)))
K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) is V16() set
K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a))) is set
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 - T) * w),(T * s)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - T) * w) + (T * s) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(1 - T) * t is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(1 - T) * t is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
T * G is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
T * G is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - T) * t) + (T * G) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 - T) * t),(T * G)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - T) * t) + (T * G) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
b . (((1 - T) * t) + (T * G)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
b . ((1 - T) * t) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
b . (T * G) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(b . ((1 - T) * t)) + (b . (T * G)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(b . ((1 - T) * t)),(b . (T * G))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(b . ((1 - T) * t)) + (b . (T * G)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
T * (b . G) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
T * (b . G) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(b . ((1 - T) * t)) + (T * (b . G)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(b . ((1 - T) * t)),(T * (b . G))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(b . ((1 - T) * t)) + (T * (b . G)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
a is ordinal natural V11() real ext-real non negative set
TOP-REAL a is non empty TopSpace-like V126() V191() V192() V209() V210() V211() V212() V213() V214() V215() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL a) is non empty set
b is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
{ (((1 - b1) * b) + (b1 * r)) where b1 is V11() real ext-real Element of REAL : 0 <= b1 } is set
K6( the carrier of (TOP-REAL a)) is set
s is set
t is V11() real ext-real Element of REAL
1 - t is V11() real ext-real Element of REAL
- t is V11() real ext-real set
1 + (- t) is V11() real ext-real set
(1 - t) * b is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(1 - t) * b is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
t * r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
t * r is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - t) * b) + (t * r) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
the U7 of (TOP-REAL a) is V16() V21() V30(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) Element of K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)))
K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)) is V16() set
K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) is V16() set
K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a))) is set
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 - t) * b),(t * r)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - t) * b) + (t * r) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
a is ordinal natural V11() real ext-real non negative V33() V34() V179() V180() V181() V182() V183() V184() Element of NAT
TOP-REAL a is non empty TopSpace-like V126() V191() V192() V209() V210() V211() V212() V213() V214() V215() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL a) is non empty set
b is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(a,b,r) is Element of K6( the carrier of (TOP-REAL a))
K6( the carrier of (TOP-REAL a)) is set
{ (((1 - b1) * b) + (b1 * r)) where b1 is V11() real ext-real Element of REAL : 0 <= b1 } is set
w is set
s is V11() real ext-real Element of REAL
1 - s is V11() real ext-real Element of REAL
- s is V11() real ext-real set
1 + (- s) is V11() real ext-real set
(1 - s) * b is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(1 - s) * b is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
s * r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
s * r is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - s) * b) + (s * r) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
the U7 of (TOP-REAL a) is V16() V21() V30(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) Element of K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)))
K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)) is V16() set
K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) is V16() set
K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a))) is set
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 - s) * b),(s * r)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - s) * b) + (s * r) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
s is V11() real ext-real set
1 - s is V11() real ext-real Element of REAL
- s is V11() real ext-real set
1 + (- s) is V11() real ext-real set
(1 - s) * b is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(1 - s) * b is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
s * r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
s * r is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - s) * b) + (s * r) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
the U7 of (TOP-REAL a) is V16() V21() V30(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) Element of K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)))
K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)) is V16() set
K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) is V16() set
K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a))) is set
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 - s) * b),(s * r)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - s) * b) + (s * r) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
a is ordinal natural V11() real ext-real non negative V33() V34() V179() V180() V181() V182() V183() V184() Element of NAT
TOP-REAL a is non empty TopSpace-like V126() V191() V192() V209() V210() V211() V212() V213() V214() V215() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL a) is non empty set
b is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(a,b,r) is Element of K6( the carrier of (TOP-REAL a))
K6( the carrier of (TOP-REAL a)) is set
{ (((1 - b1) * b) + (b1 * r)) where b1 is V11() real ext-real Element of REAL : 0 <= b1 } is set
1 - 0 is non empty V11() real ext-real positive non negative Element of REAL
- 0 is empty V11() real ext-real non positive non negative V16() non-zero V18() V19( NAT ) V20( RAT ) V21() V22() constant V24() V37() FinSequence-like FinSubsequence-like FinSequence-membered complex-yielding ext-real-valued real-valued natural-valued V179() V180() V181() V182() V183() V184() V185() set
1 + (- 0) is non empty V11() real ext-real positive non negative set
(1 - 0) * b is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(1 - 0) * b is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
0 * r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
0 * r is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - 0) * b) + (0 * r) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
the U7 of (TOP-REAL a) is V16() V21() V30(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) Element of K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)))
K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)) is V16() set
K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) is V16() set
K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a))) is set
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 - 0) * b),(0 * r)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - 0) * b) + (0 * r) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
a is ordinal natural V11() real ext-real non negative V33() V34() V179() V180() V181() V182() V183() V184() Element of NAT
TOP-REAL a is non empty TopSpace-like V126() V191() V192() V209() V210() V211() V212() V213() V214() V215() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL a) is non empty set
b is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(a,b,r) is non empty Element of K6( the carrier of (TOP-REAL a))
K6( the carrier of (TOP-REAL a)) is set
{ (((1 - b1) * b) + (b1 * r)) where b1 is V11() real ext-real Element of REAL : 0 <= b1 } is set
1 - 0 is non empty V11() real ext-real positive non negative Element of REAL
- 0 is empty V11() real ext-real non positive non negative V16() non-zero V18() V19( NAT ) V20( RAT ) V21() V22() constant V24() V37() FinSequence-like FinSubsequence-like FinSequence-membered complex-yielding ext-real-valued real-valued natural-valued V179() V180() V181() V182() V183() V184() V185() set
1 + (- 0) is non empty V11() real ext-real positive non negative set
(1 - 0) * b is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(1 - 0) * b is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
0 * r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
0 * r is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - 0) * b) + (0 * r) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
the U7 of (TOP-REAL a) is V16() V21() V30(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) Element of K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)))
K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)) is V16() set
K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) is V16() set
K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a))) is set
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 - 0) * b),(0 * r)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - 0) * b) + (0 * r) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
b + (0 * r) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),b,(0 * r)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
b + (0 * r) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
0. (TOP-REAL a) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like V69( TOP-REAL a) complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
the ZeroF of (TOP-REAL a) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
b + (0. (TOP-REAL a)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),b,(0. (TOP-REAL a))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
b + (0. (TOP-REAL a)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
a is ordinal natural V11() real ext-real non negative V33() V34() V179() V180() V181() V182() V183() V184() Element of NAT
TOP-REAL a is non empty TopSpace-like V126() V191() V192() V209() V210() V211() V212() V213() V214() V215() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL a) is non empty set
b is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(a,r,b) is non empty Element of K6( the carrier of (TOP-REAL a))
K6( the carrier of (TOP-REAL a)) is set
{ (((1 - b1) * r) + (b1 * b)) where b1 is V11() real ext-real Element of REAL : 0 <= b1 } is set
1 - 1 is V11() real ext-real Element of REAL
- 1 is V11() real ext-real non positive set
1 + (- 1) is V11() real ext-real set
(1 - 1) * r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(1 - 1) * r is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
1 * b is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
1 * b is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - 1) * r) + (1 * b) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
the U7 of (TOP-REAL a) is V16() V21() V30(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) Element of K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)))
K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)) is V16() set
K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) is V16() set
K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a))) is set
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 - 1) * r),(1 * b)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - 1) * r) + (1 * b) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
0 * r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
0 * r is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(0 * r) + b is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(0 * r),b) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(0 * r) + b is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
0. (TOP-REAL a) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like V69( TOP-REAL a) complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
the ZeroF of (TOP-REAL a) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(0. (TOP-REAL a)) + b is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(0. (TOP-REAL a)),b) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(0. (TOP-REAL a)) + b is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
a is ordinal natural V11() real ext-real non negative V33() V34() V179() V180() V181() V182() V183() V184() Element of NAT
TOP-REAL a is non empty TopSpace-like V126() V191() V192() V209() V210() V211() V212() V213() V214() V215() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL a) is non empty set
b is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(a,b,b) is non empty Element of K6( the carrier of (TOP-REAL a))
K6( the carrier of (TOP-REAL a)) is set
{ (((1 - b1) * b) + (b1 * b)) where b1 is V11() real ext-real Element of REAL : 0 <= b1 } is set
{b} is non empty V24() set
r is set
w is V11() real ext-real set
1 - w is V11() real ext-real Element of REAL
- w is V11() real ext-real set
1 + (- w) is V11() real ext-real set
(1 - w) * b is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(1 - w) * b is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
w * b is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
w * b is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - w) * b) + (w * b) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
the U7 of (TOP-REAL a) is V16() V21() V30(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) Element of K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)))
K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)) is V16() set
K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) is V16() set
K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a))) is set
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 - w) * b),(w * b)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - w) * b) + (w * b) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
r is set
a is ordinal natural V11() real ext-real non negative V33() V34() V179() V180() V181() V182() V183() V184() Element of NAT
TOP-REAL a is non empty TopSpace-like V126() V191() V192() V209() V210() V211() V212() V213() V214() V215() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL a) is non empty set
b is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(a,r,b) is non empty Element of K6( the carrier of (TOP-REAL a))
K6( the carrier of (TOP-REAL a)) is set
{ (((1 - b1) * r) + (b1 * b)) where b1 is V11() real ext-real Element of REAL : 0 <= b1 } is set
w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(a,r,w) is non empty Element of K6( the carrier of (TOP-REAL a))
{ (((1 - b1) * r) + (b1 * w)) where b1 is V11() real ext-real Element of REAL : 0 <= b1 } is set
s is V11() real ext-real set
1 - s is V11() real ext-real Element of REAL
- s is V11() real ext-real set
1 + (- s) is V11() real ext-real set
(1 - s) * r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(1 - s) * r is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
s * w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
s * w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - s) * r) + (s * w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
the U7 of (TOP-REAL a) is V16() V21() V30(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) Element of K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)))
K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)) is V16() set
K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) is V16() set
K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a))) is set
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 - s) * r),(s * w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - s) * r) + (s * w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
t is set
G is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
S is V11() real ext-real set
1 - S is V11() real ext-real Element of REAL
- S is V11() real ext-real set
1 + (- S) is V11() real ext-real set
(1 - S) * r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(1 - S) * r is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
S * b is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
S * b is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - S) * r) + (S * b) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 - S) * r),(S * b)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - S) * r) + (S * b) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
S * s is V11() real ext-real set
S * ((1 - s) * r) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
S * ((1 - s) * r) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
S * (s * w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
S * (s * w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(S * ((1 - s) * r)) + (S * (s * w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(S * ((1 - s) * r)),(S * (s * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(S * ((1 - s) * r)) + (S * (s * w)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - S) * r) + ((S * ((1 - s) * r)) + (S * (s * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 - S) * r),((S * ((1 - s) * r)) + (S * (s * w)))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - S) * r) + ((S * ((1 - s) * r)) + (S * (s * w))) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - S) * r) + (S * ((1 - s) * r)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 - S) * r),(S * ((1 - s) * r))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - S) * r) + (S * ((1 - s) * r)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((1 - S) * r) + (S * ((1 - s) * r))) + (S * (s * w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(((1 - S) * r) + (S * ((1 - s) * r))),(S * (s * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(((1 - S) * r) + (S * ((1 - s) * r))) + (S * (s * w)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
S * (1 - s) is V11() real ext-real Element of REAL
(S * (1 - s)) * r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(S * (1 - s)) * r is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - S) * r) + ((S * (1 - s)) * r) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 - S) * r),((S * (1 - s)) * r)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - S) * r) + ((S * (1 - s)) * r) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((1 - S) * r) + ((S * (1 - s)) * r)) + (S * (s * w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(((1 - S) * r) + ((S * (1 - s)) * r)),(S * (s * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(((1 - S) * r) + ((S * (1 - s)) * r)) + (S * (s * w)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(1 - S) + (S * (1 - s)) is V11() real ext-real Element of REAL
((1 - S) + (S * (1 - s))) * r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - S) + (S * (1 - s))) * r is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((1 - S) + (S * (1 - s))) * r) + (S * (s * w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(((1 - S) + (S * (1 - s))) * r),(S * (s * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(((1 - S) + (S * (1 - s))) * r) + (S * (s * w)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
1 - (S * s) is V11() real ext-real Element of REAL
- (S * s) is V11() real ext-real set
1 + (- (S * s)) is V11() real ext-real set
(1 - (S * s)) * r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(1 - (S * s)) * r is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(S * s) * w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(S * s) * w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - (S * s)) * r) + ((S * s) * w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 - (S * s)) * r),((S * s) * w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - (S * s)) * r) + ((S * s) * w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
a is ordinal natural V11() real ext-real non negative V33() V34() V179() V180() V181() V182() V183() V184() Element of NAT
TOP-REAL a is non empty TopSpace-like V126() V191() V192() V209() V210() V211() V212() V213() V214() V215() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL a) is non empty set
b is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(a,r,b) is non empty Element of K6( the carrier of (TOP-REAL a))
K6( the carrier of (TOP-REAL a)) is set
{ (((1 - b1) * r) + (b1 * b)) where b1 is V11() real ext-real Element of REAL : 0 <= b1 } is set
w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(a,r,w) is non empty Element of K6( the carrier of (TOP-REAL a))
{ (((1 - b1) * r) + (b1 * w)) where b1 is V11() real ext-real Element of REAL : 0 <= b1 } is set
s is V11() real ext-real set
1 - s is V11() real ext-real Element of REAL
- s is V11() real ext-real set
1 + (- s) is V11() real ext-real set
(1 - s) * r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(1 - s) * r is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
s * w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
s * w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - s) * r) + (s * w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
the U7 of (TOP-REAL a) is V16() V21() V30(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) Element of K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)))
K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)) is V16() set
K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) is V16() set
K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a))) is set
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 - s) * r),(s * w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - s) * r) + (s * w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
t is set
G is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
S is V11() real ext-real set
1 - S is V11() real ext-real Element of REAL
- S is V11() real ext-real set
1 + (- S) is V11() real ext-real set
(1 - S) * r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(1 - S) * r is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
S * w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
S * w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - S) * r) + (S * w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 - S) * r),(S * w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - S) * r) + (S * w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
S / s is V11() real ext-real Element of COMPLEX
s " is V11() real ext-real set
S * (s ") is V11() real ext-real set
(S / s) * s is V11() real ext-real set
1 - (S / s) is V11() real ext-real Element of REAL
- (S / s) is V11() real ext-real set
1 + (- (S / s)) is V11() real ext-real set
(S / s) * (1 - s) is V11() real ext-real Element of REAL
(1 - (S / s)) + ((S / s) * (1 - s)) is V11() real ext-real Element of REAL
((1 - (S / s)) + ((S / s) * (1 - s))) * r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - (S / s)) + ((S / s) * (1 - s))) * r is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(S / s) * (s * w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(S / s) * (s * w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((1 - (S / s)) + ((S / s) * (1 - s))) * r) + ((S / s) * (s * w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(((1 - (S / s)) + ((S / s) * (1 - s))) * r),((S / s) * (s * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(((1 - (S / s)) + ((S / s) * (1 - s))) * r) + ((S / s) * (s * w)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(1 - (S / s)) * r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(1 - (S / s)) * r is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((S / s) * (1 - s)) * r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((S / s) * (1 - s)) * r is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - (S / s)) * r) + (((S / s) * (1 - s)) * r) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 - (S / s)) * r),(((S / s) * (1 - s)) * r)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - (S / s)) * r) + (((S / s) * (1 - s)) * r) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((1 - (S / s)) * r) + (((S / s) * (1 - s)) * r)) + ((S / s) * (s * w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(((1 - (S / s)) * r) + (((S / s) * (1 - s)) * r)),((S / s) * (s * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(((1 - (S / s)) * r) + (((S / s) * (1 - s)) * r)) + ((S / s) * (s * w)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(S / s) * ((1 - s) * r) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(S / s) * ((1 - s) * r) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - (S / s)) * r) + ((S / s) * ((1 - s) * r)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 - (S / s)) * r),((S / s) * ((1 - s) * r))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - (S / s)) * r) + ((S / s) * ((1 - s) * r)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((1 - (S / s)) * r) + ((S / s) * ((1 - s) * r))) + ((S / s) * (s * w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(((1 - (S / s)) * r) + ((S / s) * ((1 - s) * r))),((S / s) * (s * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(((1 - (S / s)) * r) + ((S / s) * ((1 - s) * r))) + ((S / s) * (s * w)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((S / s) * ((1 - s) * r)) + ((S / s) * (s * w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((S / s) * ((1 - s) * r)),((S / s) * (s * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((S / s) * ((1 - s) * r)) + ((S / s) * (s * w)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - (S / s)) * r) + (((S / s) * ((1 - s) * r)) + ((S / s) * (s * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 - (S / s)) * r),(((S / s) * ((1 - s) * r)) + ((S / s) * (s * w)))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - (S / s)) * r) + (((S / s) * ((1 - s) * r)) + ((S / s) * (s * w))) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(S / s) * (((1 - s) * r) + (s * w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(S / s) * (((1 - s) * r) + (s * w)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - (S / s)) * r) + ((S / s) * (((1 - s) * r) + (s * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 - (S / s)) * r),((S / s) * (((1 - s) * r) + (s * w)))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - (S / s)) * r) + ((S / s) * (((1 - s) * r) + (s * w))) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
a is ordinal natural V11() real ext-real non negative V33() V34() V179() V180() V181() V182() V183() V184() Element of NAT
TOP-REAL a is non empty TopSpace-like V126() V191() V192() V209() V210() V211() V212() V213() V214() V215() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL a) is non empty set
b is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
LSeg (b,r) is Element of K6( the carrier of (TOP-REAL a))
K6( the carrier of (TOP-REAL a)) is set
{ (((1 - b1) * b) + (b1 * r)) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
(a,b,r) is non empty Element of K6( the carrier of (TOP-REAL a))
{ (((1 - b1) * b) + (b1 * r)) where b1 is V11() real ext-real Element of REAL : 0 <= b1 } is set
w is set
s is V11() real ext-real Element of REAL
1 - s is V11() real ext-real Element of REAL
- s is V11() real ext-real set
1 + (- s) is V11() real ext-real set
(1 - s) * b is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(1 - s) * b is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
s * r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
s * r is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - s) * b) + (s * r) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
the U7 of (TOP-REAL a) is V16() V21() V30(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) Element of K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)))
K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)) is V16() set
K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) is V16() set
K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a))) is set
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 - s) * b),(s * r)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - s) * b) + (s * r) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
a is ordinal natural V11() real ext-real non negative V33() V34() V179() V180() V181() V182() V183() V184() Element of NAT
TOP-REAL a is non empty TopSpace-like V126() V191() V192() V209() V210() V211() V212() V213() V214() V215() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL a) is non empty set
b is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(a,b,r) is non empty Element of K6( the carrier of (TOP-REAL a))
K6( the carrier of (TOP-REAL a)) is set
{ (((1 - b1) * b) + (b1 * r)) where b1 is V11() real ext-real Element of REAL : 0 <= b1 } is set
w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
s is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
LSeg (w,s) is Element of K6( the carrier of (TOP-REAL a))
{ (((1 - b1) * w) + (b1 * s)) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
G is V11() real ext-real set
1 - G is V11() real ext-real Element of REAL
- G is V11() real ext-real set
1 + (- G) is V11() real ext-real set
(1 - G) * b is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(1 - G) * b is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
G * r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
G * r is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - G) * b) + (G * r) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
the U7 of (TOP-REAL a) is V16() V21() V30(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) Element of K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)))
K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)) is V16() set
K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) is V16() set
K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a))) is set
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 - G) * b),(G * r)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - G) * b) + (G * r) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
S is V11() real ext-real set
1 - S is V11() real ext-real Element of REAL
- S is V11() real ext-real set
1 + (- S) is V11() real ext-real set
(1 - S) * b is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(1 - S) * b is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
S * r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
S * r is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - S) * b) + (S * r) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 - S) * b),(S * r)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - S) * b) + (S * r) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
T is set
Y is V11() real ext-real Element of REAL
1 - Y is V11() real ext-real Element of REAL
- Y is V11() real ext-real set
1 + (- Y) is V11() real ext-real set
(1 - Y) * w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(1 - Y) * w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
Y * s is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
Y * s is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - Y) * w) + (Y * s) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 - Y) * w),(Y * s)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - Y) * w) + (Y * s) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(1 - Y) * G is V11() real ext-real Element of REAL
Y * S is V11() real ext-real Element of REAL
((1 - Y) * G) + (Y * S) is V11() real ext-real Element of REAL
Y - Y is V11() real ext-real Element of REAL
Y + (- Y) is V11() real ext-real set
(1 - Y) * ((1 - G) * b) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(1 - Y) * ((1 - G) * b) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(1 - Y) * (G * r) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(1 - Y) * (G * r) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - Y) * ((1 - G) * b)) + ((1 - Y) * (G * r)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 - Y) * ((1 - G) * b)),((1 - Y) * (G * r))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - Y) * ((1 - G) * b)) + ((1 - Y) * (G * r)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
Y * (((1 - S) * b) + (S * r)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
Y * (((1 - S) * b) + (S * r)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((1 - Y) * ((1 - G) * b)) + ((1 - Y) * (G * r))) + (Y * (((1 - S) * b) + (S * r))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(((1 - Y) * ((1 - G) * b)) + ((1 - Y) * (G * r))),(Y * (((1 - S) * b) + (S * r)))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(((1 - Y) * ((1 - G) * b)) + ((1 - Y) * (G * r))) + (Y * (((1 - S) * b) + (S * r))) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
Y * ((1 - S) * b) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
Y * ((1 - S) * b) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
Y * (S * r) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
Y * (S * r) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(Y * ((1 - S) * b)) + (Y * (S * r)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(Y * ((1 - S) * b)),(Y * (S * r))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(Y * ((1 - S) * b)) + (Y * (S * r)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((1 - Y) * ((1 - G) * b)) + ((1 - Y) * (G * r))) + ((Y * ((1 - S) * b)) + (Y * (S * r))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(((1 - Y) * ((1 - G) * b)) + ((1 - Y) * (G * r))),((Y * ((1 - S) * b)) + (Y * (S * r)))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(((1 - Y) * ((1 - G) * b)) + ((1 - Y) * (G * r))) + ((Y * ((1 - S) * b)) + (Y * (S * r))) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - Y) * ((1 - G) * b)) + ((Y * ((1 - S) * b)) + (Y * (S * r))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 - Y) * ((1 - G) * b)),((Y * ((1 - S) * b)) + (Y * (S * r)))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - Y) * ((1 - G) * b)) + ((Y * ((1 - S) * b)) + (Y * (S * r))) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((1 - Y) * ((1 - G) * b)) + ((Y * ((1 - S) * b)) + (Y * (S * r)))) + ((1 - Y) * (G * r)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(((1 - Y) * ((1 - G) * b)) + ((Y * ((1 - S) * b)) + (Y * (S * r)))),((1 - Y) * (G * r))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(((1 - Y) * ((1 - G) * b)) + ((Y * ((1 - S) * b)) + (Y * (S * r)))) + ((1 - Y) * (G * r)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - Y) * ((1 - G) * b)) + (Y * ((1 - S) * b)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 - Y) * ((1 - G) * b)),(Y * ((1 - S) * b))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - Y) * ((1 - G) * b)) + (Y * ((1 - S) * b)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((1 - Y) * ((1 - G) * b)) + (Y * ((1 - S) * b))) + (Y * (S * r)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(((1 - Y) * ((1 - G) * b)) + (Y * ((1 - S) * b))),(Y * (S * r))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(((1 - Y) * ((1 - G) * b)) + (Y * ((1 - S) * b))) + (Y * (S * r)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((((1 - Y) * ((1 - G) * b)) + (Y * ((1 - S) * b))) + (Y * (S * r))) + ((1 - Y) * (G * r)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((((1 - Y) * ((1 - G) * b)) + (Y * ((1 - S) * b))) + (Y * (S * r))),((1 - Y) * (G * r))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((((1 - Y) * ((1 - G) * b)) + (Y * ((1 - S) * b))) + (Y * (S * r))) + ((1 - Y) * (G * r)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(1 - Y) * (1 - G) is V11() real ext-real Element of REAL
((1 - Y) * (1 - G)) * b is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - Y) * (1 - G)) * b is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((1 - Y) * (1 - G)) * b) + (Y * ((1 - S) * b)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(((1 - Y) * (1 - G)) * b),(Y * ((1 - S) * b))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(((1 - Y) * (1 - G)) * b) + (Y * ((1 - S) * b)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((((1 - Y) * (1 - G)) * b) + (Y * ((1 - S) * b))) + (Y * (S * r)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((((1 - Y) * (1 - G)) * b) + (Y * ((1 - S) * b))),(Y * (S * r))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((((1 - Y) * (1 - G)) * b) + (Y * ((1 - S) * b))) + (Y * (S * r)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((((1 - Y) * (1 - G)) * b) + (Y * ((1 - S) * b))) + (Y * (S * r))) + ((1 - Y) * (G * r)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(((((1 - Y) * (1 - G)) * b) + (Y * ((1 - S) * b))) + (Y * (S * r))),((1 - Y) * (G * r))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(((((1 - Y) * (1 - G)) * b) + (Y * ((1 - S) * b))) + (Y * (S * r))) + ((1 - Y) * (G * r)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
Y * (1 - S) is V11() real ext-real Element of REAL
(Y * (1 - S)) * b is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(Y * (1 - S)) * b is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((1 - Y) * (1 - G)) * b) + ((Y * (1 - S)) * b) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(((1 - Y) * (1 - G)) * b),((Y * (1 - S)) * b)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(((1 - Y) * (1 - G)) * b) + ((Y * (1 - S)) * b) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((((1 - Y) * (1 - G)) * b) + ((Y * (1 - S)) * b)) + (Y * (S * r)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((((1 - Y) * (1 - G)) * b) + ((Y * (1 - S)) * b)),(Y * (S * r))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((((1 - Y) * (1 - G)) * b) + ((Y * (1 - S)) * b)) + (Y * (S * r)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((((1 - Y) * (1 - G)) * b) + ((Y * (1 - S)) * b)) + (Y * (S * r))) + ((1 - Y) * (G * r)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(((((1 - Y) * (1 - G)) * b) + ((Y * (1 - S)) * b)) + (Y * (S * r))),((1 - Y) * (G * r))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(((((1 - Y) * (1 - G)) * b) + ((Y * (1 - S)) * b)) + (Y * (S * r))) + ((1 - Y) * (G * r)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(Y * S) * r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(Y * S) * r is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((((1 - Y) * (1 - G)) * b) + ((Y * (1 - S)) * b)) + ((Y * S) * r) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((((1 - Y) * (1 - G)) * b) + ((Y * (1 - S)) * b)),((Y * S) * r)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((((1 - Y) * (1 - G)) * b) + ((Y * (1 - S)) * b)) + ((Y * S) * r) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((((1 - Y) * (1 - G)) * b) + ((Y * (1 - S)) * b)) + ((Y * S) * r)) + ((1 - Y) * (G * r)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(((((1 - Y) * (1 - G)) * b) + ((Y * (1 - S)) * b)) + ((Y * S) * r)),((1 - Y) * (G * r))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(((((1 - Y) * (1 - G)) * b) + ((Y * (1 - S)) * b)) + ((Y * S) * r)) + ((1 - Y) * (G * r)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - Y) * G) * r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - Y) * G) * r is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((((1 - Y) * (1 - G)) * b) + ((Y * (1 - S)) * b)) + ((Y * S) * r)) + (((1 - Y) * G) * r) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(((((1 - Y) * (1 - G)) * b) + ((Y * (1 - S)) * b)) + ((Y * S) * r)),(((1 - Y) * G) * r)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(((((1 - Y) * (1 - G)) * b) + ((Y * (1 - S)) * b)) + ((Y * S) * r)) + (((1 - Y) * G) * r) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - Y) * (1 - G)) + (Y * (1 - S)) is V11() real ext-real Element of REAL
(((1 - Y) * (1 - G)) + (Y * (1 - S))) * b is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(((1 - Y) * (1 - G)) + (Y * (1 - S))) * b is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((((1 - Y) * (1 - G)) + (Y * (1 - S))) * b) + ((Y * S) * r) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((((1 - Y) * (1 - G)) + (Y * (1 - S))) * b),((Y * S) * r)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((((1 - Y) * (1 - G)) + (Y * (1 - S))) * b) + ((Y * S) * r) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((((1 - Y) * (1 - G)) + (Y * (1 - S))) * b) + ((Y * S) * r)) + (((1 - Y) * G) * r) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(((((1 - Y) * (1 - G)) + (Y * (1 - S))) * b) + ((Y * S) * r)),(((1 - Y) * G) * r)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(((((1 - Y) * (1 - G)) + (Y * (1 - S))) * b) + ((Y * S) * r)) + (((1 - Y) * G) * r) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((Y * S) * r) + (((1 - Y) * G) * r) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((Y * S) * r),(((1 - Y) * G) * r)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((Y * S) * r) + (((1 - Y) * G) * r) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((((1 - Y) * (1 - G)) + (Y * (1 - S))) * b) + (((Y * S) * r) + (((1 - Y) * G) * r)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((((1 - Y) * (1 - G)) + (Y * (1 - S))) * b),(((Y * S) * r) + (((1 - Y) * G) * r))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((((1 - Y) * (1 - G)) + (Y * (1 - S))) * b) + (((Y * S) * r) + (((1 - Y) * G) * r)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
1 - (((1 - Y) * G) + (Y * S)) is V11() real ext-real Element of REAL
- (((1 - Y) * G) + (Y * S)) is V11() real ext-real set
1 + (- (((1 - Y) * G) + (Y * S))) is V11() real ext-real set
(1 - (((1 - Y) * G) + (Y * S))) * b is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(1 - (((1 - Y) * G) + (Y * S))) * b is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((1 - Y) * G) + (Y * S)) * r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(((1 - Y) * G) + (Y * S)) * r is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - (((1 - Y) * G) + (Y * S))) * b) + ((((1 - Y) * G) + (Y * S)) * r) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 - (((1 - Y) * G) + (Y * S))) * b),((((1 - Y) * G) + (Y * S)) * r)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - (((1 - Y) * G) + (Y * S))) * b) + ((((1 - Y) * G) + (Y * S)) * r) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
a is ordinal natural V11() real ext-real non negative V33() V34() V179() V180() V181() V182() V183() V184() Element of NAT
TOP-REAL a is non empty TopSpace-like V126() V191() V192() V209() V210() V211() V212() V213() V214() V215() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL a) is non empty set
b is V11() real ext-real set
r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
{r} is non empty V24() set
w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(a,w,b) is closed bounded Element of K6( the carrier of (TOP-REAL a))
K6( the carrier of (TOP-REAL a)) is set
{ b1 where b1 is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a) : |.(b1 - w).| = b } is set
(a,w,b) is open bounded convex Element of K6( the carrier of (TOP-REAL a))
{ b1 where b1 is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a) : not b <= |.(b1 - w).| } is set
s is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
LSeg (r,s) is Element of K6( the carrier of (TOP-REAL a))
{ (((1 - b1) * r) + (b1 * s)) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
(LSeg (r,s)) /\ (a,w,b) is Element of K6( the carrier of (TOP-REAL a))
S is set
T is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
Y is V11() real ext-real Element of REAL
1 - Y is V11() real ext-real Element of REAL
- Y is V11() real ext-real set
1 + (- Y) is V11() real ext-real set
(1 - Y) * r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(1 - Y) * r is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
Y * s is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
Y * s is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - Y) * r) + (Y * s) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
the U7 of (TOP-REAL a) is V16() V21() V30(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) Element of K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)))
K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)) is V16() set
K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) is V16() set
K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a))) is set
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 - Y) * r),(Y * s)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - Y) * r) + (Y * s) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
s - w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
- 1 is V11() real ext-real non positive set
(- 1) * w is V16() V21() set
K382((TOP-REAL a),s,(- w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),s,(- w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
s + (- w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
s - w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K448(w) is V16() V21() complex-yielding set
K419(s,K448(w)) is V16() V21() set
Y * (s - w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
Y * (s - w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
|.(Y * (s - w)).| is V11() real ext-real non negative Element of REAL
sqr (Y * (s - w)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt ((Y * (s - w)),(Y * (s - w))) is V16() V21() set
Sum (sqr (Y * (s - w))) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (Y * (s - w)))) is V11() real ext-real Element of REAL
abs Y is V11() real ext-real Element of REAL
|.(s - w).| is V11() real ext-real non negative Element of REAL
sqr (s - w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt ((s - w),(s - w)) is V16() V21() set
Sum (sqr (s - w)) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (s - w))) is V11() real ext-real Element of REAL
(abs Y) * |.(s - w).| is V11() real ext-real Element of REAL
Y * |.(s - w).| is V11() real ext-real Element of REAL
Y - 1 is V11() real ext-real Element of REAL
Y + (- 1) is V11() real ext-real set
1 - 1 is V11() real ext-real Element of REAL
1 + (- 1) is V11() real ext-real set
- 0 is empty V11() real ext-real non positive non negative V16() non-zero V18() V19( NAT ) V20( RAT ) V21() V22() constant V24() V37() FinSequence-like FinSubsequence-like FinSequence-membered complex-yielding ext-real-valued real-valued natural-valued V179() V180() V181() V182() V183() V184() V185() set
- (Y - 1) is V11() real ext-real Element of REAL
r - w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K382((TOP-REAL a),r,(- w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),r,(- w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
r + (- w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
r - w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K419(r,K448(w)) is V16() V21() set
(1 - Y) * (r - w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(1 - Y) * (r - w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
|.((1 - Y) * (r - w)).| is V11() real ext-real non negative Element of REAL
sqr ((1 - Y) * (r - w)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt (((1 - Y) * (r - w)),((1 - Y) * (r - w))) is V16() V21() set
Sum (sqr ((1 - Y) * (r - w))) is V11() real ext-real Element of REAL
sqrt (Sum (sqr ((1 - Y) * (r - w)))) is V11() real ext-real Element of REAL
abs (1 - Y) is V11() real ext-real Element of REAL
|.(r - w).| is V11() real ext-real non negative Element of REAL
sqr (r - w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt ((r - w),(r - w)) is V16() V21() set
Sum (sqr (r - w)) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (r - w))) is V11() real ext-real Element of REAL
(abs (1 - Y)) * |.(r - w).| is V11() real ext-real Element of REAL
(1 - Y) * |.(r - w).| is V11() real ext-real Element of REAL
(1 - Y) * b is V11() real ext-real Element of REAL
T - w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K382((TOP-REAL a),T,(- w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),T,(- w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
T + (- w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
T - w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K419(T,K448(w)) is V16() V21() set
|.(T - w).| is V11() real ext-real non negative Element of REAL
sqr (T - w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt ((T - w),(T - w)) is V16() V21() set
Sum (sqr (T - w)) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (T - w))) is V11() real ext-real Element of REAL
(1 - Y) + Y is V11() real ext-real Element of REAL
((1 - Y) + Y) * w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - Y) + Y) * w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((1 - Y) * r) + (Y * s)) - (((1 - Y) + Y) * w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- (((1 - Y) + Y) * w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- (((1 - Y) + Y) * w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(- 1) * (((1 - Y) + Y) * w) is V16() V21() set
K382((TOP-REAL a),(((1 - Y) * r) + (Y * s)),(- (((1 - Y) + Y) * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(((1 - Y) * r) + (Y * s)),(- (((1 - Y) + Y) * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(((1 - Y) * r) + (Y * s)) + (- (((1 - Y) + Y) * w)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((1 - Y) * r) + (Y * s)) - (((1 - Y) + Y) * w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K448((((1 - Y) + Y) * w)) is V16() V21() complex-yielding set
K419((((1 - Y) * r) + (Y * s)),K448((((1 - Y) + Y) * w))) is V16() V21() set
|.((((1 - Y) * r) + (Y * s)) - (((1 - Y) + Y) * w)).| is V11() real ext-real non negative Element of REAL
sqr ((((1 - Y) * r) + (Y * s)) - (((1 - Y) + Y) * w)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt (((((1 - Y) * r) + (Y * s)) - (((1 - Y) + Y) * w)),((((1 - Y) * r) + (Y * s)) - (((1 - Y) + Y) * w))) is V16() V21() set
Sum (sqr ((((1 - Y) * r) + (Y * s)) - (((1 - Y) + Y) * w))) is V11() real ext-real Element of REAL
sqrt (Sum (sqr ((((1 - Y) * r) + (Y * s)) - (((1 - Y) + Y) * w)))) is V11() real ext-real Element of REAL
(1 - Y) * w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(1 - Y) * w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
Y * w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
Y * w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - Y) * w) + (Y * w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 - Y) * w),(Y * w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - Y) * w) + (Y * w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((1 - Y) * r) + (Y * s)) - (((1 - Y) * w) + (Y * w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- (((1 - Y) * w) + (Y * w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- (((1 - Y) * w) + (Y * w)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(- 1) * (((1 - Y) * w) + (Y * w)) is V16() V21() set
K382((TOP-REAL a),(((1 - Y) * r) + (Y * s)),(- (((1 - Y) * w) + (Y * w)))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(((1 - Y) * r) + (Y * s)),(- (((1 - Y) * w) + (Y * w)))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(((1 - Y) * r) + (Y * s)) + (- (((1 - Y) * w) + (Y * w))) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((1 - Y) * r) + (Y * s)) - (((1 - Y) * w) + (Y * w)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K448((((1 - Y) * w) + (Y * w))) is V16() V21() complex-yielding set
K419((((1 - Y) * r) + (Y * s)),K448((((1 - Y) * w) + (Y * w)))) is V16() V21() set
|.((((1 - Y) * r) + (Y * s)) - (((1 - Y) * w) + (Y * w))).| is V11() real ext-real non negative Element of REAL
sqr ((((1 - Y) * r) + (Y * s)) - (((1 - Y) * w) + (Y * w))) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt (((((1 - Y) * r) + (Y * s)) - (((1 - Y) * w) + (Y * w))),((((1 - Y) * r) + (Y * s)) - (((1 - Y) * w) + (Y * w)))) is V16() V21() set
Sum (sqr ((((1 - Y) * r) + (Y * s)) - (((1 - Y) * w) + (Y * w)))) is V11() real ext-real Element of REAL
sqrt (Sum (sqr ((((1 - Y) * r) + (Y * s)) - (((1 - Y) * w) + (Y * w))))) is V11() real ext-real Element of REAL
(((1 - Y) * r) + (Y * s)) - ((1 - Y) * w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- ((1 - Y) * w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- ((1 - Y) * w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(- 1) * ((1 - Y) * w) is V16() V21() set
K382((TOP-REAL a),(((1 - Y) * r) + (Y * s)),(- ((1 - Y) * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(((1 - Y) * r) + (Y * s)),(- ((1 - Y) * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(((1 - Y) * r) + (Y * s)) + (- ((1 - Y) * w)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((1 - Y) * r) + (Y * s)) - ((1 - Y) * w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K448(((1 - Y) * w)) is V16() V21() complex-yielding set
K419((((1 - Y) * r) + (Y * s)),K448(((1 - Y) * w))) is V16() V21() set
((((1 - Y) * r) + (Y * s)) - ((1 - Y) * w)) - (Y * w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- (Y * w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- (Y * w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(- 1) * (Y * w) is V16() V21() set
K382((TOP-REAL a),((((1 - Y) * r) + (Y * s)) - ((1 - Y) * w)),(- (Y * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((((1 - Y) * r) + (Y * s)) - ((1 - Y) * w)),(- (Y * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((((1 - Y) * r) + (Y * s)) - ((1 - Y) * w)) + (- (Y * w)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((((1 - Y) * r) + (Y * s)) - ((1 - Y) * w)) - (Y * w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K448((Y * w)) is V16() V21() complex-yielding set
K419(((((1 - Y) * r) + (Y * s)) - ((1 - Y) * w)),K448((Y * w))) is V16() V21() set
|.(((((1 - Y) * r) + (Y * s)) - ((1 - Y) * w)) - (Y * w)).| is V11() real ext-real non negative Element of REAL
sqr (((((1 - Y) * r) + (Y * s)) - ((1 - Y) * w)) - (Y * w)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt ((((((1 - Y) * r) + (Y * s)) - ((1 - Y) * w)) - (Y * w)),(((((1 - Y) * r) + (Y * s)) - ((1 - Y) * w)) - (Y * w))) is V16() V21() set
Sum (sqr (((((1 - Y) * r) + (Y * s)) - ((1 - Y) * w)) - (Y * w))) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (((((1 - Y) * r) + (Y * s)) - ((1 - Y) * w)) - (Y * w)))) is V11() real ext-real Element of REAL
((1 - Y) * r) - ((1 - Y) * w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K382((TOP-REAL a),((1 - Y) * r),(- ((1 - Y) * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 - Y) * r),(- ((1 - Y) * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - Y) * r) + (- ((1 - Y) * w)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - Y) * r) - ((1 - Y) * w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K419(((1 - Y) * r),K448(((1 - Y) * w))) is V16() V21() set
(((1 - Y) * r) - ((1 - Y) * w)) + (Y * s) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(((1 - Y) * r) - ((1 - Y) * w)),(Y * s)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(((1 - Y) * r) - ((1 - Y) * w)) + (Y * s) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((((1 - Y) * r) - ((1 - Y) * w)) + (Y * s)) - (Y * w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K382((TOP-REAL a),((((1 - Y) * r) - ((1 - Y) * w)) + (Y * s)),(- (Y * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((((1 - Y) * r) - ((1 - Y) * w)) + (Y * s)),(- (Y * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((((1 - Y) * r) - ((1 - Y) * w)) + (Y * s)) + (- (Y * w)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((((1 - Y) * r) - ((1 - Y) * w)) + (Y * s)) - (Y * w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K419(((((1 - Y) * r) - ((1 - Y) * w)) + (Y * s)),K448((Y * w))) is V16() V21() set
|.(((((1 - Y) * r) - ((1 - Y) * w)) + (Y * s)) - (Y * w)).| is V11() real ext-real non negative Element of REAL
sqr (((((1 - Y) * r) - ((1 - Y) * w)) + (Y * s)) - (Y * w)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt ((((((1 - Y) * r) - ((1 - Y) * w)) + (Y * s)) - (Y * w)),(((((1 - Y) * r) - ((1 - Y) * w)) + (Y * s)) - (Y * w))) is V16() V21() set
Sum (sqr (((((1 - Y) * r) - ((1 - Y) * w)) + (Y * s)) - (Y * w))) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (((((1 - Y) * r) - ((1 - Y) * w)) + (Y * s)) - (Y * w)))) is V11() real ext-real Element of REAL
((1 - Y) * (r - w)) + (Y * s) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 - Y) * (r - w)),(Y * s)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - Y) * (r - w)) + (Y * s) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((1 - Y) * (r - w)) + (Y * s)) - (Y * w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K382((TOP-REAL a),(((1 - Y) * (r - w)) + (Y * s)),(- (Y * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(((1 - Y) * (r - w)) + (Y * s)),(- (Y * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(((1 - Y) * (r - w)) + (Y * s)) + (- (Y * w)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((1 - Y) * (r - w)) + (Y * s)) - (Y * w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K419((((1 - Y) * (r - w)) + (Y * s)),K448((Y * w))) is V16() V21() set
|.((((1 - Y) * (r - w)) + (Y * s)) - (Y * w)).| is V11() real ext-real non negative Element of REAL
sqr ((((1 - Y) * (r - w)) + (Y * s)) - (Y * w)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt (((((1 - Y) * (r - w)) + (Y * s)) - (Y * w)),((((1 - Y) * (r - w)) + (Y * s)) - (Y * w))) is V16() V21() set
Sum (sqr ((((1 - Y) * (r - w)) + (Y * s)) - (Y * w))) is V11() real ext-real Element of REAL
sqrt (Sum (sqr ((((1 - Y) * (r - w)) + (Y * s)) - (Y * w)))) is V11() real ext-real Element of REAL
(Y * s) - (Y * w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K382((TOP-REAL a),(Y * s),(- (Y * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(Y * s),(- (Y * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(Y * s) + (- (Y * w)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(Y * s) - (Y * w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K419((Y * s),K448((Y * w))) is V16() V21() set
((1 - Y) * (r - w)) + ((Y * s) - (Y * w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 - Y) * (r - w)),((Y * s) - (Y * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - Y) * (r - w)) + ((Y * s) - (Y * w)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
|.(((1 - Y) * (r - w)) + ((Y * s) - (Y * w))).| is V11() real ext-real non negative Element of REAL
sqr (((1 - Y) * (r - w)) + ((Y * s) - (Y * w))) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt ((((1 - Y) * (r - w)) + ((Y * s) - (Y * w))),(((1 - Y) * (r - w)) + ((Y * s) - (Y * w)))) is V16() V21() set
Sum (sqr (((1 - Y) * (r - w)) + ((Y * s) - (Y * w)))) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (((1 - Y) * (r - w)) + ((Y * s) - (Y * w))))) is V11() real ext-real Element of REAL
((1 - Y) * (r - w)) + (Y * (s - w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 - Y) * (r - w)),(Y * (s - w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - Y) * (r - w)) + (Y * (s - w)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
|.(((1 - Y) * (r - w)) + (Y * (s - w))).| is V11() real ext-real non negative Element of REAL
sqr (((1 - Y) * (r - w)) + (Y * (s - w))) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt ((((1 - Y) * (r - w)) + (Y * (s - w))),(((1 - Y) * (r - w)) + (Y * (s - w)))) is V16() V21() set
Sum (sqr (((1 - Y) * (r - w)) + (Y * (s - w)))) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (((1 - Y) * (r - w)) + (Y * (s - w))))) is V11() real ext-real Element of REAL
Y * b is V11() real ext-real Element of REAL
((1 - Y) * b) + (Y * b) is V11() real ext-real Element of REAL
((1 - Y) * b) + (Y * |.(s - w).|) is V11() real ext-real Element of REAL
1 * r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
1 * r is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
0. (TOP-REAL a) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like V69( TOP-REAL a) complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
the ZeroF of (TOP-REAL a) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(1 * r) + (0. (TOP-REAL a)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(1 * r),(0. (TOP-REAL a))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(1 * r) + (0. (TOP-REAL a)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
S is set
a is ordinal natural V11() real ext-real non negative V33() V34() V179() V180() V181() V182() V183() V184() Element of NAT
TOP-REAL a is non empty TopSpace-like V126() V191() V192() V209() V210() V211() V212() V213() V214() V215() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL a) is non empty set
b is V11() real ext-real set
r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(a,w,b) is closed bounded Element of K6( the carrier of (TOP-REAL a))
K6( the carrier of (TOP-REAL a)) is set
{ b1 where b1 is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a) : |.(b1 - w).| = b } is set
(a,w,b) is open bounded convex Element of K6( the carrier of (TOP-REAL a))
{ b1 where b1 is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a) : not b <= |.(b1 - w).| } is set
s is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
LSeg (r,s) is Element of K6( the carrier of (TOP-REAL a))
{ (((1 - b1) * r) + (b1 * s)) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
{r,s} is non empty V24() set
(LSeg (r,s)) \ {r,s} is Element of K6( the carrier of (TOP-REAL a))
{r} is non empty V24() set
REAL a is non empty V24() FinSequence-membered FinSequenceSet of REAL
a -tuples_on REAL is V24() FinSequence-membered FinSequenceSet of REAL
G is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of a -tuples_on REAL
S is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of a -tuples_on REAL
t is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of a -tuples_on REAL
r - w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
- 1 is V11() real ext-real non positive set
(- 1) * w is V16() V21() set
K382((TOP-REAL a),r,(- w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
the U7 of (TOP-REAL a) is V16() V21() V30(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) Element of K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)))
K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)) is V16() set
K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) is V16() set
K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a))) is set
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),r,(- w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
r + (- w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
r - w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K448(w) is V16() V21() complex-yielding set
K419(r,K448(w)) is V16() V21() set
s - w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K382((TOP-REAL a),s,(- w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),s,(- w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
s + (- w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
s - w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K419(s,K448(w)) is V16() V21() set
|((r - w),(s - w))| is V11() real ext-real Element of REAL
e1 is set
S - t is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of a -tuples_on REAL
K448(t) is V16() V21() complex-yielding set
(- 1) * t is V16() V21() set
K419(S,K448(t)) is V16() V21() set
sqr (S - t) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of a -tuples_on REAL
mlt ((S - t),(S - t)) is V16() V21() set
Sum (sqr (S - t)) is V11() real ext-real Element of REAL
X is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
|.X.| is V11() real ext-real non negative Element of REAL
sqr X is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt (X,X) is V16() V21() set
Sum (sqr X) is V11() real ext-real Element of REAL
sqrt (Sum (sqr X)) is V11() real ext-real Element of REAL
|.X.| ^2 is V11() real ext-real Element of REAL
|.X.| * |.X.| is V11() real ext-real non negative set
|.(s - w).| is V11() real ext-real non negative Element of REAL
sqr (s - w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt ((s - w),(s - w)) is V16() V21() set
Sum (sqr (s - w)) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (s - w))) is V11() real ext-real Element of REAL
|.(s - w).| ^2 is V11() real ext-real Element of REAL
|.(s - w).| * |.(s - w).| is V11() real ext-real non negative set
b ^2 is V11() real ext-real set
b * b is V11() real ext-real set
l is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
m is V11() real ext-real Element of REAL
1 - m is V11() real ext-real Element of REAL
- m is V11() real ext-real set
1 + (- m) is V11() real ext-real set
(1 - m) * r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(1 - m) * r is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
m * s is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
m * s is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - m) * r) + (m * s) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 - m) * r),(m * s)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - m) * r) + (m * s) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(1 - m) * (r - w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(1 - m) * (r - w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
m * (s - w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
m * (s - w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
G - S is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of a -tuples_on REAL
K448(S) is V16() V21() complex-yielding set
(- 1) * S is V16() V21() set
K419(G,K448(S)) is V16() V21() set
sqr (G - S) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of a -tuples_on REAL
mlt ((G - S),(G - S)) is V16() V21() set
Sum (sqr (G - S)) is V11() real ext-real Element of REAL
l - w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K382((TOP-REAL a),l,(- w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),l,(- w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
l + (- w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
l - w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K419(l,K448(w)) is V16() V21() set
o is V16() V19( NAT ) V20( REAL ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL a
W2 is V16() V19( NAT ) V20( REAL ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL a
o + W2 is V16() V19( NAT ) V20( REAL ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL a
(1 - m) * w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(1 - m) * w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - m) * r) - ((1 - m) * w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- ((1 - m) * w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- ((1 - m) * w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(- 1) * ((1 - m) * w) is V16() V21() set
K382((TOP-REAL a),((1 - m) * r),(- ((1 - m) * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 - m) * r),(- ((1 - m) * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - m) * r) + (- ((1 - m) * w)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - m) * r) - ((1 - m) * w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K448(((1 - m) * w)) is V16() V21() complex-yielding set
K419(((1 - m) * r),K448(((1 - m) * w))) is V16() V21() set
(((1 - m) * r) - ((1 - m) * w)) + (m * (s - w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(((1 - m) * r) - ((1 - m) * w)),(m * (s - w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(((1 - m) * r) - ((1 - m) * w)) + (m * (s - w)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
m * w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
m * w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(m * s) - (m * w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- (m * w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- (m * w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(- 1) * (m * w) is V16() V21() set
K382((TOP-REAL a),(m * s),(- (m * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(m * s),(- (m * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(m * s) + (- (m * w)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(m * s) - (m * w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K448((m * w)) is V16() V21() complex-yielding set
K419((m * s),K448((m * w))) is V16() V21() set
(((1 - m) * r) - ((1 - m) * w)) + ((m * s) - (m * w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(((1 - m) * r) - ((1 - m) * w)),((m * s) - (m * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(((1 - m) * r) - ((1 - m) * w)) + ((m * s) - (m * w)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((1 - m) * r) - ((1 - m) * w)) + (m * s) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(((1 - m) * r) - ((1 - m) * w)),(m * s)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(((1 - m) * r) - ((1 - m) * w)) + (m * s) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((((1 - m) * r) - ((1 - m) * w)) + (m * s)) - (m * w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K382((TOP-REAL a),((((1 - m) * r) - ((1 - m) * w)) + (m * s)),(- (m * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((((1 - m) * r) - ((1 - m) * w)) + (m * s)),(- (m * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((((1 - m) * r) - ((1 - m) * w)) + (m * s)) + (- (m * w)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((((1 - m) * r) - ((1 - m) * w)) + (m * s)) - (m * w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K419(((((1 - m) * r) - ((1 - m) * w)) + (m * s)),K448((m * w))) is V16() V21() set
(((1 - m) * r) + (m * s)) - ((1 - m) * w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K382((TOP-REAL a),(((1 - m) * r) + (m * s)),(- ((1 - m) * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(((1 - m) * r) + (m * s)),(- ((1 - m) * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(((1 - m) * r) + (m * s)) + (- ((1 - m) * w)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((1 - m) * r) + (m * s)) - ((1 - m) * w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K419((((1 - m) * r) + (m * s)),K448(((1 - m) * w))) is V16() V21() set
((((1 - m) * r) + (m * s)) - ((1 - m) * w)) - (m * w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K382((TOP-REAL a),((((1 - m) * r) + (m * s)) - ((1 - m) * w)),(- (m * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((((1 - m) * r) + (m * s)) - ((1 - m) * w)),(- (m * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((((1 - m) * r) + (m * s)) - ((1 - m) * w)) + (- (m * w)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((((1 - m) * r) + (m * s)) - ((1 - m) * w)) - (m * w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K419(((((1 - m) * r) + (m * s)) - ((1 - m) * w)),K448((m * w))) is V16() V21() set
((1 - m) * w) + (m * w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 - m) * w),(m * w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - m) * w) + (m * w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((1 - m) * r) + (m * s)) - (((1 - m) * w) + (m * w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- (((1 - m) * w) + (m * w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- (((1 - m) * w) + (m * w)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(- 1) * (((1 - m) * w) + (m * w)) is V16() V21() set
K382((TOP-REAL a),(((1 - m) * r) + (m * s)),(- (((1 - m) * w) + (m * w)))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(((1 - m) * r) + (m * s)),(- (((1 - m) * w) + (m * w)))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(((1 - m) * r) + (m * s)) + (- (((1 - m) * w) + (m * w))) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((1 - m) * r) + (m * s)) - (((1 - m) * w) + (m * w)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K448((((1 - m) * w) + (m * w))) is V16() V21() complex-yielding set
K419((((1 - m) * r) + (m * s)),K448((((1 - m) * w) + (m * w)))) is V16() V21() set
1 * w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
1 * w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(1 * w) - (m * w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K382((TOP-REAL a),(1 * w),(- (m * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(1 * w),(- (m * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(1 * w) + (- (m * w)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(1 * w) - (m * w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K419((1 * w),K448((m * w))) is V16() V21() set
((1 * w) - (m * w)) + (m * w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 * w) - (m * w)),(m * w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 * w) - (m * w)) + (m * w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((1 - m) * r) + (m * s)) - (((1 * w) - (m * w)) + (m * w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- (((1 * w) - (m * w)) + (m * w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- (((1 * w) - (m * w)) + (m * w)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(- 1) * (((1 * w) - (m * w)) + (m * w)) is V16() V21() set
K382((TOP-REAL a),(((1 - m) * r) + (m * s)),(- (((1 * w) - (m * w)) + (m * w)))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(((1 - m) * r) + (m * s)),(- (((1 * w) - (m * w)) + (m * w)))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(((1 - m) * r) + (m * s)) + (- (((1 * w) - (m * w)) + (m * w))) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((1 - m) * r) + (m * s)) - (((1 * w) - (m * w)) + (m * w)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K448((((1 * w) - (m * w)) + (m * w))) is V16() V21() complex-yielding set
K419((((1 - m) * r) + (m * s)),K448((((1 * w) - (m * w)) + (m * w)))) is V16() V21() set
(((1 - m) * r) + (m * s)) - (1 * w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- (1 * w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- (1 * w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(- 1) * (1 * w) is V16() V21() set
K382((TOP-REAL a),(((1 - m) * r) + (m * s)),(- (1 * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(((1 - m) * r) + (m * s)),(- (1 * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(((1 - m) * r) + (m * s)) + (- (1 * w)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((1 - m) * r) + (m * s)) - (1 * w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K448((1 * w)) is V16() V21() complex-yielding set
K419((((1 - m) * r) + (m * s)),K448((1 * w))) is V16() V21() set
Rf is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
W1 is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of a -tuples_on REAL
W2 is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of a -tuples_on REAL
mlt (W1,W2) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of a -tuples_on REAL
G - t is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of a -tuples_on REAL
K419(G,K448(t)) is V16() V21() set
m * (S - t) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of a -tuples_on REAL
mlt ((G - t),(m * (S - t))) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of a -tuples_on REAL
(1 - m) * (mlt ((G - t),(m * (S - t)))) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of a -tuples_on REAL
sqr W1 is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of a -tuples_on REAL
mlt (W1,W1) is V16() V21() set
sqr (G - t) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of a -tuples_on REAL
mlt ((G - t),(G - t)) is V16() V21() set
(1 - m) ^2 is V11() real ext-real Element of REAL
(1 - m) * (1 - m) is V11() real ext-real set
((1 - m) ^2) * (sqr (G - t)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of a -tuples_on REAL
sqr Rf is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt (Rf,Rf) is V16() V21() set
Sum (sqr Rf) is V11() real ext-real Element of REAL
|.(l - w).| is V11() real ext-real non negative Element of REAL
sqr (l - w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt ((l - w),(l - w)) is V16() V21() set
Sum (sqr (l - w)) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (l - w))) is V11() real ext-real Element of REAL
|.(l - w).| ^2 is V11() real ext-real Element of REAL
|.(l - w).| * |.(l - w).| is V11() real ext-real non negative set
2 * (mlt (W1,W2)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of a -tuples_on REAL
(sqr W1) + (2 * (mlt (W1,W2))) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of a -tuples_on REAL
sqr W2 is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of a -tuples_on REAL
mlt (W2,W2) is V16() V21() set
((sqr W1) + (2 * (mlt (W1,W2)))) + (sqr W2) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of a -tuples_on REAL
Sum (((sqr W1) + (2 * (mlt (W1,W2)))) + (sqr W2)) is V11() real ext-real Element of REAL
Sum ((sqr W1) + (2 * (mlt (W1,W2)))) is V11() real ext-real Element of REAL
Sum (sqr W2) is V11() real ext-real Element of REAL
(Sum ((sqr W1) + (2 * (mlt (W1,W2))))) + (Sum (sqr W2)) is V11() real ext-real Element of REAL
Sum (sqr W1) is V11() real ext-real Element of REAL
Sum (2 * (mlt (W1,W2))) is V11() real ext-real Element of REAL
(Sum (sqr W1)) + (Sum (2 * (mlt (W1,W2)))) is V11() real ext-real Element of REAL
((Sum (sqr W1)) + (Sum (2 * (mlt (W1,W2))))) + (Sum (sqr W2)) is V11() real ext-real Element of REAL
Sum (sqr (G - t)) is V11() real ext-real Element of REAL
((1 - m) ^2) * (Sum (sqr (G - t))) is V11() real ext-real Element of REAL
(((1 - m) ^2) * (Sum (sqr (G - t)))) + (Sum (2 * (mlt (W1,W2)))) is V11() real ext-real Element of REAL
sqr (m * (S - t)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of a -tuples_on REAL
mlt ((m * (S - t)),(m * (S - t))) is V16() V21() set
Sum (sqr (m * (S - t))) is V11() real ext-real Element of REAL
((((1 - m) ^2) * (Sum (sqr (G - t)))) + (Sum (2 * (mlt (W1,W2))))) + (Sum (sqr (m * (S - t)))) is V11() real ext-real Element of REAL
m ^2 is V11() real ext-real Element of REAL
m * m is V11() real ext-real set
(m ^2) * (sqr (S - t)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of a -tuples_on REAL
Sum ((m ^2) * (sqr (S - t))) is V11() real ext-real Element of REAL
((((1 - m) ^2) * (Sum (sqr (G - t)))) + (Sum (2 * (mlt (W1,W2))))) + (Sum ((m ^2) * (sqr (S - t)))) is V11() real ext-real Element of REAL
(m ^2) * (Sum (sqr (S - t))) is V11() real ext-real Element of REAL
((((1 - m) ^2) * (Sum (sqr (G - t)))) + (Sum (2 * (mlt (W1,W2))))) + ((m ^2) * (Sum (sqr (S - t)))) is V11() real ext-real Element of REAL
t is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
|.t.| is V11() real ext-real non negative Element of REAL
sqr t is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt (t,t) is V16() V21() set
Sum (sqr t) is V11() real ext-real Element of REAL
sqrt (Sum (sqr t)) is V11() real ext-real Element of REAL
|.t.| ^2 is V11() real ext-real Element of REAL
|.t.| * |.t.| is V11() real ext-real non negative set
((1 - m) ^2) * (|.t.| ^2) is V11() real ext-real Element of REAL
(((1 - m) ^2) * (|.t.| ^2)) + (Sum (2 * (mlt (W1,W2)))) is V11() real ext-real Element of REAL
((((1 - m) ^2) * (|.t.| ^2)) + (Sum (2 * (mlt (W1,W2))))) + ((m ^2) * (Sum (sqr (S - t)))) is V11() real ext-real Element of REAL
((1 - m) ^2) * (b ^2) is V11() real ext-real Element of REAL
(((1 - m) ^2) * (b ^2)) + (Sum (2 * (mlt (W1,W2)))) is V11() real ext-real Element of REAL
(m ^2) * (|.X.| ^2) is V11() real ext-real Element of REAL
((((1 - m) ^2) * (b ^2)) + (Sum (2 * (mlt (W1,W2))))) + ((m ^2) * (|.X.| ^2)) is V11() real ext-real Element of REAL
Sum (mlt (W1,W2)) is V11() real ext-real Element of REAL
2 * (Sum (mlt (W1,W2))) is V11() real ext-real Element of REAL
(((1 - m) ^2) * (b ^2)) + (2 * (Sum (mlt (W1,W2)))) is V11() real ext-real Element of REAL
(m ^2) * (b ^2) is V11() real ext-real Element of REAL
((((1 - m) ^2) * (b ^2)) + (2 * (Sum (mlt (W1,W2))))) + ((m ^2) * (b ^2)) is V11() real ext-real Element of REAL
mlt ((G - t),(S - t)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of a -tuples_on REAL
m * (mlt ((G - t),(S - t))) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of a -tuples_on REAL
(1 - m) * (m * (mlt ((G - t),(S - t)))) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of a -tuples_on REAL
Sum ((1 - m) * (m * (mlt ((G - t),(S - t))))) is V11() real ext-real Element of REAL
2 * (Sum ((1 - m) * (m * (mlt ((G - t),(S - t)))))) is V11() real ext-real Element of REAL
(((1 - m) ^2) * (b ^2)) + (2 * (Sum ((1 - m) * (m * (mlt ((G - t),(S - t))))))) is V11() real ext-real Element of REAL
((((1 - m) ^2) * (b ^2)) + (2 * (Sum ((1 - m) * (m * (mlt ((G - t),(S - t)))))))) + ((m ^2) * (b ^2)) is V11() real ext-real Element of REAL
(1 - m) * m is V11() real ext-real Element of REAL
((1 - m) * m) * (mlt ((G - t),(S - t))) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of a -tuples_on REAL
Sum (((1 - m) * m) * (mlt ((G - t),(S - t)))) is V11() real ext-real Element of REAL
2 * (Sum (((1 - m) * m) * (mlt ((G - t),(S - t))))) is V11() real ext-real Element of REAL
(((1 - m) ^2) * (b ^2)) + (2 * (Sum (((1 - m) * m) * (mlt ((G - t),(S - t)))))) is V11() real ext-real Element of REAL
((((1 - m) ^2) * (b ^2)) + (2 * (Sum (((1 - m) * m) * (mlt ((G - t),(S - t))))))) + ((m ^2) * (b ^2)) is V11() real ext-real Element of REAL
Sum (mlt ((G - t),(S - t))) is V11() real ext-real Element of REAL
((1 - m) * m) * (Sum (mlt ((G - t),(S - t)))) is V11() real ext-real Element of REAL
2 * (((1 - m) * m) * (Sum (mlt ((G - t),(S - t))))) is V11() real ext-real Element of REAL
(((1 - m) ^2) * (b ^2)) + (2 * (((1 - m) * m) * (Sum (mlt ((G - t),(S - t)))))) is V11() real ext-real Element of REAL
((((1 - m) ^2) * (b ^2)) + (2 * (((1 - m) * m) * (Sum (mlt ((G - t),(S - t))))))) + ((m ^2) * (b ^2)) is V11() real ext-real Element of REAL
2 * (1 - m) is V11() real ext-real Element of REAL
(2 * (1 - m)) * m is V11() real ext-real Element of REAL
((2 * (1 - m)) * m) * (Sum (mlt ((G - t),(S - t)))) is V11() real ext-real Element of REAL
(((1 - m) ^2) * (b ^2)) + (((2 * (1 - m)) * m) * (Sum (mlt ((G - t),(S - t))))) is V11() real ext-real Element of REAL
((((1 - m) ^2) * (b ^2)) + (((2 * (1 - m)) * m) * (Sum (mlt ((G - t),(S - t)))))) + ((m ^2) * (b ^2)) is V11() real ext-real Element of REAL
((2 * (1 - m)) * m) * |((r - w),(s - w))| is V11() real ext-real Element of REAL
(((1 - m) ^2) * (b ^2)) + (((2 * (1 - m)) * m) * |((r - w),(s - w))|) is V11() real ext-real Element of REAL
((((1 - m) ^2) * (b ^2)) + (((2 * (1 - m)) * m) * |((r - w),(s - w))|)) + ((m ^2) * (b ^2)) is V11() real ext-real Element of REAL
2 * m is V11() real ext-real Element of REAL
1 - (2 * m) is V11() real ext-real Element of REAL
- (2 * m) is V11() real ext-real set
1 + (- (2 * m)) is V11() real ext-real set
(1 - (2 * m)) + (m ^2) is V11() real ext-real Element of REAL
((1 - (2 * m)) + (m ^2)) + (m ^2) is V11() real ext-real Element of REAL
(((1 - (2 * m)) + (m ^2)) + (m ^2)) * (b ^2) is V11() real ext-real Element of REAL
(2 * m) * (1 - m) is V11() real ext-real Element of REAL
((2 * m) * (1 - m)) * |((r - w),(s - w))| is V11() real ext-real Element of REAL
((((1 - (2 * m)) + (m ^2)) + (m ^2)) * (b ^2)) + (((2 * m) * (1 - m)) * |((r - w),(s - w))|) is V11() real ext-real Element of REAL
(|.(l - w).| ^2) - (b ^2) is V11() real ext-real Element of REAL
- (b ^2) is V11() real ext-real set
(|.(l - w).| ^2) + (- (b ^2)) is V11() real ext-real set
(- (b ^2)) + |((r - w),(s - w))| is V11() real ext-real Element of REAL
((2 * m) * (1 - m)) * ((- (b ^2)) + |((r - w),(s - w))|) is V11() real ext-real Element of REAL
1 - 1 is V11() real ext-real Element of REAL
1 + (- 1) is V11() real ext-real set
|.(r - w).| is V11() real ext-real non negative Element of REAL
sqr (r - w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt ((r - w),(r - w)) is V16() V21() set
Sum (sqr (r - w)) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (r - w))) is V11() real ext-real Element of REAL
|.(r - w).| ^2 is V11() real ext-real Element of REAL
|.(r - w).| * |.(r - w).| is V11() real ext-real non negative set
|((r - w),(s - w))| - (b ^2) is V11() real ext-real Element of REAL
|((r - w),(s - w))| + (- (b ^2)) is V11() real ext-real set
2 * |((r - w),(s - w))| is V11() real ext-real Element of REAL
(|.(r - w).| ^2) - (2 * |((r - w),(s - w))|) is V11() real ext-real Element of REAL
- (2 * |((r - w),(s - w))|) is V11() real ext-real set
(|.(r - w).| ^2) + (- (2 * |((r - w),(s - w))|)) is V11() real ext-real set
((|.(r - w).| ^2) - (2 * |((r - w),(s - w))|)) + (|.(s - w).| ^2) is V11() real ext-real Element of REAL
(r - w) - (s - w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- (s - w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- (s - w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(- 1) * (s - w) is V16() V21() set
K382((TOP-REAL a),(r - w),(- (s - w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(r - w),(- (s - w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(r - w) + (- (s - w)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(r - w) - (s - w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K448((s - w)) is V16() V21() complex-yielding set
K419((r - w),K448((s - w))) is V16() V21() set
|.((r - w) - (s - w)).| is V11() real ext-real non negative Element of REAL
sqr ((r - w) - (s - w)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt (((r - w) - (s - w)),((r - w) - (s - w))) is V16() V21() set
Sum (sqr ((r - w) - (s - w))) is V11() real ext-real Element of REAL
sqrt (Sum (sqr ((r - w) - (s - w)))) is V11() real ext-real Element of REAL
|.((r - w) - (s - w)).| ^2 is V11() real ext-real Element of REAL
|.((r - w) - (s - w)).| * |.((r - w) - (s - w)).| is V11() real ext-real non negative set
(r - w) - s is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- s is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- s is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(- 1) * s is V16() V21() set
K382((TOP-REAL a),(r - w),(- s)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(r - w),(- s)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(r - w) + (- s) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(r - w) - s is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K448(s) is V16() V21() complex-yielding set
K419((r - w),K448(s)) is V16() V21() set
((r - w) - s) + w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((r - w) - s),w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((r - w) - s) + w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
|.(((r - w) - s) + w).| is V11() real ext-real non negative Element of REAL
sqr (((r - w) - s) + w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt ((((r - w) - s) + w),(((r - w) - s) + w)) is V16() V21() set
Sum (sqr (((r - w) - s) + w)) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (((r - w) - s) + w))) is V11() real ext-real Element of REAL
|.(((r - w) - s) + w).| ^2 is V11() real ext-real Element of REAL
|.(((r - w) - s) + w).| * |.(((r - w) - s) + w).| is V11() real ext-real non negative set
(r - w) + w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(r - w),w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(r - w) + w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((r - w) + w) - s is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K382((TOP-REAL a),((r - w) + w),(- s)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((r - w) + w),(- s)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((r - w) + w) + (- s) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((r - w) + w) - s is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K419(((r - w) + w),K448(s)) is V16() V21() set
|.(((r - w) + w) - s).| is V11() real ext-real non negative Element of REAL
sqr (((r - w) + w) - s) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt ((((r - w) + w) - s),(((r - w) + w) - s)) is V16() V21() set
Sum (sqr (((r - w) + w) - s)) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (((r - w) + w) - s))) is V11() real ext-real Element of REAL
|.(((r - w) + w) - s).| ^2 is V11() real ext-real Element of REAL
|.(((r - w) + w) - s).| * |.(((r - w) + w) - s).| is V11() real ext-real non negative set
|.(G - S).| is V11() real ext-real non negative Element of REAL
sqr (G - S) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
Sum (sqr (G - S)) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (G - S))) is V11() real ext-real Element of REAL
|.(G - S).| ^2 is V11() real ext-real Element of REAL
|.(G - S).| * |.(G - S).| is V11() real ext-real non negative set
a |-> 0 is V16() V19( NAT ) V21() V37() FinSequence-like FinSubsequence-like set
(a,w,b) is closed bounded convex Element of K6( the carrier of (TOP-REAL a))
{ b1 where b1 is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a) : |.(b1 - w).| <= b } is set
a is ordinal natural V11() real ext-real non negative V33() V34() V179() V180() V181() V182() V183() V184() Element of NAT
TOP-REAL a is non empty TopSpace-like V126() V191() V192() V209() V210() V211() V212() V213() V214() V215() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL a) is non empty set
b is V11() real ext-real set
r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(a,w,b) is closed bounded Element of K6( the carrier of (TOP-REAL a))
K6( the carrier of (TOP-REAL a)) is set
{ b1 where b1 is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a) : |.(b1 - w).| = b } is set
s is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
LSeg (r,s) is Element of K6( the carrier of (TOP-REAL a))
{ (((1 - b1) * r) + (b1 * s)) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
(LSeg (r,s)) /\ (a,w,b) is Element of K6( the carrier of (TOP-REAL a))
{r,s} is non empty V24() set
(LSeg (r,s)) \ {r,s} is Element of K6( the carrier of (TOP-REAL a))
(a,w,b) is open bounded convex Element of K6( the carrier of (TOP-REAL a))
{ b1 where b1 is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a) : not b <= |.(b1 - w).| } is set
t is set
t is set
a is ordinal natural V11() real ext-real non negative V33() V34() V179() V180() V181() V182() V183() V184() Element of NAT
TOP-REAL a is non empty TopSpace-like V126() V191() V192() V209() V210() V211() V212() V213() V214() V215() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL a) is non empty set
b is V11() real ext-real set
r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(a,w,b) is closed bounded Element of K6( the carrier of (TOP-REAL a))
K6( the carrier of (TOP-REAL a)) is set
{ b1 where b1 is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a) : |.(b1 - w).| = b } is set
s is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(a,r,s) is non empty convex Element of K6( the carrier of (TOP-REAL a))
{ (((1 - b1) * r) + (b1 * s)) where b1 is V11() real ext-real Element of REAL : 0 <= b1 } is set
(a,r,s) /\ (a,w,b) is Element of K6( the carrier of (TOP-REAL a))
{r,s} is non empty V24() set
{r} is non empty V24() set
t is set
t is set
t is set
S is V11() real ext-real set
1 - S is V11() real ext-real Element of REAL
- S is V11() real ext-real set
1 + (- S) is V11() real ext-real set
(1 - S) * r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(1 - S) * r is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
S * s is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
S * s is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - S) * r) + (S * s) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
the U7 of (TOP-REAL a) is V16() V21() V30(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) Element of K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)))
K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)) is V16() set
K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) is V16() set
K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a))) is set
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 - S) * r),(S * s)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - S) * r) + (S * s) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
T is V11() real ext-real Element of REAL
T is V11() real ext-real Element of REAL
T is V11() real ext-real Element of REAL
G is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
LSeg (r,s) is Element of K6( the carrier of (TOP-REAL a))
{ (((1 - b1) * r) + (b1 * s)) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
(LSeg (r,s)) \ {r,s} is Element of K6( the carrier of (TOP-REAL a))
(a,w,b) is open bounded convex Element of K6( the carrier of (TOP-REAL a))
{ b1 where b1 is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a) : not b <= |.(b1 - w).| } is set
G - w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
- 1 is V11() real ext-real non positive set
(- 1) * w is V16() V21() set
K382((TOP-REAL a),G,(- w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),G,(- w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
G + (- w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
G - w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K448(w) is V16() V21() complex-yielding set
K419(G,K448(w)) is V16() V21() set
|.(G - w).| is V11() real ext-real non negative Element of REAL
sqr (G - w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt ((G - w),(G - w)) is V16() V21() set
Sum (sqr (G - w)) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (G - w))) is V11() real ext-real Element of REAL
T is V11() real ext-real Element of REAL
1 / T is V11() real ext-real Element of REAL
T " is V11() real ext-real set
1 * (T ") is V11() real ext-real set
1 - (1 / T) is V11() real ext-real Element of REAL
- (1 / T) is V11() real ext-real set
1 + (- (1 / T)) is V11() real ext-real set
(1 - (1 / T)) * r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(1 - (1 / T)) * r is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
G is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(1 / T) * G is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(1 / T) * G is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - (1 / T)) * r) + ((1 / T) * G) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 - (1 / T)) * r),((1 / T) * G)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - (1 / T)) * r) + ((1 / T) * G) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
1 - T is V11() real ext-real Element of REAL
- T is V11() real ext-real set
1 + (- T) is V11() real ext-real set
(1 - T) * r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(1 - T) * r is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(1 / T) * ((1 - T) * r) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(1 / T) * ((1 - T) * r) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
T * s is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
T * s is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(1 / T) * (T * s) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(1 / T) * (T * s) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 / T) * ((1 - T) * r)) + ((1 / T) * (T * s)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 / T) * ((1 - T) * r)),((1 / T) * (T * s))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 / T) * ((1 - T) * r)) + ((1 / T) * (T * s)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - (1 / T)) * r) + (((1 / T) * ((1 - T) * r)) + ((1 / T) * (T * s))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 - (1 / T)) * r),(((1 / T) * ((1 - T) * r)) + ((1 / T) * (T * s)))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - (1 / T)) * r) + (((1 / T) * ((1 - T) * r)) + ((1 / T) * (T * s))) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(1 / T) * T is V11() real ext-real Element of REAL
((1 / T) * T) * s is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 / T) * T) * s is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 / T) * ((1 - T) * r)) + (((1 / T) * T) * s) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 / T) * ((1 - T) * r)),(((1 / T) * T) * s)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 / T) * ((1 - T) * r)) + (((1 / T) * T) * s) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - (1 / T)) * r) + (((1 / T) * ((1 - T) * r)) + (((1 / T) * T) * s)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 - (1 / T)) * r),(((1 / T) * ((1 - T) * r)) + (((1 / T) * T) * s))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - (1 / T)) * r) + (((1 / T) * ((1 - T) * r)) + (((1 / T) * T) * s)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
1 * s is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
1 * s is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 / T) * ((1 - T) * r)) + (1 * s) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 / T) * ((1 - T) * r)),(1 * s)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 / T) * ((1 - T) * r)) + (1 * s) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - (1 / T)) * r) + (((1 / T) * ((1 - T) * r)) + (1 * s)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 - (1 / T)) * r),(((1 / T) * ((1 - T) * r)) + (1 * s))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - (1 / T)) * r) + (((1 / T) * ((1 - T) * r)) + (1 * s)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 / T) * ((1 - T) * r)) + s is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 / T) * ((1 - T) * r)),s) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 / T) * ((1 - T) * r)) + s is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - (1 / T)) * r) + (((1 / T) * ((1 - T) * r)) + s) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 - (1 / T)) * r),(((1 / T) * ((1 - T) * r)) + s)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - (1 / T)) * r) + (((1 / T) * ((1 - T) * r)) + s) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - (1 / T)) * r) + ((1 / T) * ((1 - T) * r)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 - (1 / T)) * r),((1 / T) * ((1 - T) * r))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - (1 / T)) * r) + ((1 / T) * ((1 - T) * r)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((1 - (1 / T)) * r) + ((1 / T) * ((1 - T) * r))) + s is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(((1 - (1 / T)) * r) + ((1 / T) * ((1 - T) * r))),s) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(((1 - (1 / T)) * r) + ((1 / T) * ((1 - T) * r))) + s is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(1 / T) * (1 - T) is V11() real ext-real Element of REAL
((1 / T) * (1 - T)) * r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 / T) * (1 - T)) * r is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - (1 / T)) * r) + (((1 / T) * (1 - T)) * r) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 - (1 / T)) * r),(((1 / T) * (1 - T)) * r)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - (1 / T)) * r) + (((1 / T) * (1 - T)) * r) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((1 - (1 / T)) * r) + (((1 / T) * (1 - T)) * r)) + s is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(((1 - (1 / T)) * r) + (((1 / T) * (1 - T)) * r)),s) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(((1 - (1 / T)) * r) + (((1 / T) * (1 - T)) * r)) + s is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(1 - (1 / T)) + ((1 / T) * (1 - T)) is V11() real ext-real Element of REAL
((1 - (1 / T)) + ((1 / T) * (1 - T))) * r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - (1 / T)) + ((1 / T) * (1 - T))) * r is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((1 - (1 / T)) + ((1 / T) * (1 - T))) * r) + s is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(((1 - (1 / T)) + ((1 / T) * (1 - T))) * r),s) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(((1 - (1 / T)) + ((1 / T) * (1 - T))) * r) + s is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(1 / T) * 1 is V11() real ext-real Element of REAL
(1 - (1 / T)) + ((1 / T) * 1) is V11() real ext-real Element of REAL
((1 - (1 / T)) + ((1 / T) * 1)) - ((1 / T) * T) is V11() real ext-real Element of REAL
- ((1 / T) * T) is V11() real ext-real set
((1 - (1 / T)) + ((1 / T) * 1)) + (- ((1 / T) * T)) is V11() real ext-real set
(((1 - (1 / T)) + ((1 / T) * 1)) - ((1 / T) * T)) * r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(((1 - (1 / T)) + ((1 / T) * 1)) - ((1 / T) * T)) * r is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((((1 - (1 / T)) + ((1 / T) * 1)) - ((1 / T) * T)) * r) + s is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((((1 - (1 / T)) + ((1 / T) * 1)) - ((1 / T) * T)) * r),s) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((((1 - (1 / T)) + ((1 / T) * 1)) - ((1 / T) * T)) * r) + s is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - (1 / T)) + ((1 / T) * 1)) - 1 is V11() real ext-real Element of REAL
- 1 is V11() real ext-real non positive set
((1 - (1 / T)) + ((1 / T) * 1)) + (- 1) is V11() real ext-real set
(((1 - (1 / T)) + ((1 / T) * 1)) - 1) * r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(((1 - (1 / T)) + ((1 / T) * 1)) - 1) * r is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((((1 - (1 / T)) + ((1 / T) * 1)) - 1) * r) + s is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((((1 - (1 / T)) + ((1 / T) * 1)) - 1) * r),s) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((((1 - (1 / T)) + ((1 / T) * 1)) - 1) * r) + s is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
0. (TOP-REAL a) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like V69( TOP-REAL a) complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
the ZeroF of (TOP-REAL a) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(0. (TOP-REAL a)) + s is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(0. (TOP-REAL a)),s) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(0. (TOP-REAL a)) + s is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
{r,G} is non empty V24() set
LSeg (r,G) is Element of K6( the carrier of (TOP-REAL a))
{ (((1 - b1) * r) + (b1 * G)) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
(LSeg (r,G)) \ {r,G} is Element of K6( the carrier of (TOP-REAL a))
(a,w,b) is open bounded convex Element of K6( the carrier of (TOP-REAL a))
{ b1 where b1 is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a) : not b <= |.(b1 - w).| } is set
s - w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(- 1) * w is V16() V21() set
K382((TOP-REAL a),s,(- w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),s,(- w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
s + (- w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
s - w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K448(w) is V16() V21() complex-yielding set
K419(s,K448(w)) is V16() V21() set
|.(s - w).| is V11() real ext-real non negative Element of REAL
sqr (s - w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt ((s - w),(s - w)) is V16() V21() set
Sum (sqr (s - w)) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (s - w))) is V11() real ext-real Element of REAL
T is V11() real ext-real Element of REAL
t is set
a is ordinal natural V11() real ext-real non negative V33() V34() V179() V180() V181() V182() V183() V184() Element of NAT
TOP-REAL a is non empty TopSpace-like V126() V191() V192() V209() V210() V211() V212() V213() V214() V215() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL a) is non empty set
REAL a is non empty V24() FinSequence-membered FinSequenceSet of REAL
a -tuples_on REAL is V24() FinSequence-membered FinSequenceSet of REAL
b is V11() real ext-real set
b ^2 is V11() real ext-real set
b * b is V11() real ext-real set
r is V11() real ext-real set
1 - r is V11() real ext-real Element of REAL
- r is V11() real ext-real set
1 + (- r) is V11() real ext-real set
w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(1 - r) * w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(1 - r) * w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
s is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
s - w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
- 1 is V11() real ext-real non positive set
(- 1) * w is V16() V21() set
K382((TOP-REAL a),s,(- w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
the U7 of (TOP-REAL a) is V16() V21() V30(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) Element of K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)))
K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)) is V16() set
K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) is V16() set
K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a))) is set
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),s,(- w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
s + (- w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
s - w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K448(w) is V16() V21() complex-yielding set
K419(s,K448(w)) is V16() V21() set
(a,w,s) is non empty convex Element of K6( the carrier of (TOP-REAL a))
K6( the carrier of (TOP-REAL a)) is set
{ (((1 - b1) * w) + (b1 * s)) where b1 is V11() real ext-real Element of REAL : 0 <= b1 } is set
r * s is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
r * s is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - r) * w) + (r * s) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 - r) * w),(r * s)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - r) * w) + (r * s) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
t is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(a,t,b) is open bounded convex Element of K6( the carrier of (TOP-REAL a))
{ b1 where b1 is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a) : not b <= |.(b1 - t).| } is set
w - t is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- t is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- t is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(- 1) * t is V16() V21() set
K382((TOP-REAL a),w,(- t)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),w,(- t)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
w + (- t) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
w - t is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K448(t) is V16() V21() complex-yielding set
K419(w,K448(t)) is V16() V21() set
|((s - w),(w - t))| is V11() real ext-real Element of REAL
2 * |((s - w),(w - t))| is V11() real ext-real Element of REAL
- (2 * |((s - w),(w - t))|) is V11() real ext-real Element of REAL
(a,t,b) is closed bounded Element of K6( the carrier of (TOP-REAL a))
{ b1 where b1 is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a) : |.(b1 - t).| = b } is set
(a,w,s) /\ (a,t,b) is Element of K6( the carrier of (TOP-REAL a))
G is V16() V19( NAT ) V20( REAL ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL a
S is V16() V19( NAT ) V20( REAL ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL a
T is V16() V19( NAT ) V20( REAL ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL a
S - G is V16() V19( NAT ) V20( REAL ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL a
K448(G) is V16() V21() complex-yielding set
(- 1) * G is V16() V21() set
K419(S,K448(G)) is V16() V21() set
sqr (S - G) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of a -tuples_on REAL
mlt ((S - G),(S - G)) is V16() V21() set
Sum (sqr (S - G)) is V11() real ext-real Element of REAL
G - T is V16() V19( NAT ) V20( REAL ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL a
K448(T) is V16() V21() complex-yielding set
(- 1) * T is V16() V21() set
K419(G,K448(T)) is V16() V21() set
sqr (G - T) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of a -tuples_on REAL
mlt ((G - T),(G - T)) is V16() V21() set
Sum (sqr (G - T)) is V11() real ext-real Element of REAL
(Sum (sqr (G - T))) - (b ^2) is V11() real ext-real Element of REAL
- (b ^2) is V11() real ext-real set
(Sum (sqr (G - T))) + (- (b ^2)) is V11() real ext-real set
delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2))) is V11() real ext-real Element of REAL
sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))) is V11() real ext-real Element of REAL
(- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2))))) is V11() real ext-real Element of REAL
2 * (Sum (sqr (S - G))) is V11() real ext-real Element of REAL
((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G)))) is V11() real ext-real Element of REAL
(2 * (Sum (sqr (S - G)))) " is V11() real ext-real set
((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) * ((2 * (Sum (sqr (S - G)))) ") is V11() real ext-real set
|.(S - G).| is V11() real ext-real non negative Element of REAL
sqr (S - G) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
Sum (sqr (S - G)) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (S - G))) is V11() real ext-real Element of REAL
|.(S - G).| ^2 is V11() real ext-real Element of REAL
|.(S - G).| * |.(S - G).| is V11() real ext-real non negative set
|.(G - T).| is V11() real ext-real non negative Element of REAL
sqr (G - T) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
Sum (sqr (G - T)) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (G - T))) is V11() real ext-real Element of REAL
|.(G - T).| ^2 is V11() real ext-real Element of REAL
|.(G - T).| * |.(G - T).| is V11() real ext-real non negative set
|.(w - t).| is V11() real ext-real non negative Element of REAL
sqr (w - t) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt ((w - t),(w - t)) is V16() V21() set
Sum (sqr (w - t)) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (w - t))) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (G - T))) is V11() real ext-real Element of REAL
(sqrt (Sum (sqr (G - T)))) ^2 is V11() real ext-real Element of REAL
(sqrt (Sum (sqr (G - T)))) * (sqrt (Sum (sqr (G - T)))) is V11() real ext-real set
((Sum (sqr (G - T))) - (b ^2)) / (Sum (sqr (S - G))) is V11() real ext-real Element of REAL
(Sum (sqr (S - G))) " is V11() real ext-real set
((Sum (sqr (G - T))) - (b ^2)) * ((Sum (sqr (S - G))) ") is V11() real ext-real set
(- (2 * |((s - w),(w - t))|)) - (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2))))) is V11() real ext-real Element of REAL
- (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2))))) is V11() real ext-real set
(- (2 * |((s - w),(w - t))|)) + (- (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) is V11() real ext-real set
((- (2 * |((s - w),(w - t))|)) - (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G)))) is V11() real ext-real Element of REAL
((- (2 * |((s - w),(w - t))|)) - (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) * ((2 * (Sum (sqr (S - G)))) ") is V11() real ext-real set
1 - (((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) is V11() real ext-real Element of REAL
- (((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) is V11() real ext-real set
1 + (- (((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G)))))) is V11() real ext-real set
(1 - (((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G)))))) * w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(1 - (((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G)))))) * w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - (((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G)))))) * w) + ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 - (((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G)))))) * w),((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - (((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G)))))) * w) + ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
m is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
{m} is non empty V24() set
- b is V11() real ext-real set
- (- b) is V11() real ext-real set
(2 * |((s - w),(w - t))|) ^2 is V11() real ext-real Element of REAL
(2 * |((s - w),(w - t))|) * (2 * |((s - w),(w - t))|) is V11() real ext-real set
4 * (Sum (sqr (S - G))) is V11() real ext-real Element of REAL
(4 * (Sum (sqr (S - G)))) * ((Sum (sqr (G - T))) - (b ^2)) is V11() real ext-real Element of REAL
((2 * |((s - w),(w - t))|) ^2) - ((4 * (Sum (sqr (S - G)))) * ((Sum (sqr (G - T))) - (b ^2))) is V11() real ext-real Element of REAL
- ((4 * (Sum (sqr (S - G)))) * ((Sum (sqr (G - T))) - (b ^2))) is V11() real ext-real set
((2 * |((s - w),(w - t))|) ^2) + (- ((4 * (Sum (sqr (S - G)))) * ((Sum (sqr (G - T))) - (b ^2)))) is V11() real ext-real set
M is V11() real ext-real set
Polynom ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)),M) is set
Quard ((Sum (sqr (S - G))),(((- (2 * |((s - w),(w - t))|)) - (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))),(((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))),M) is set
M ^2 is V11() real ext-real set
M * M is V11() real ext-real set
(Sum (sqr (S - G))) * (M ^2) is V11() real ext-real Element of REAL
(2 * |((s - w),(w - t))|) * M is V11() real ext-real Element of REAL
((Sum (sqr (S - G))) * (M ^2)) + ((2 * |((s - w),(w - t))|) * M) is V11() real ext-real Element of REAL
(((Sum (sqr (S - G))) * (M ^2)) + ((2 * |((s - w),(w - t))|) * M)) + ((Sum (sqr (G - T))) - (b ^2)) is V11() real ext-real Element of REAL
M - (((- (2 * |((s - w),(w - t))|)) - (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) is V11() real ext-real Element of REAL
- (((- (2 * |((s - w),(w - t))|)) - (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) is V11() real ext-real set
M + (- (((- (2 * |((s - w),(w - t))|)) - (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G)))))) is V11() real ext-real set
(Sum (sqr (S - G))) * (M - (((- (2 * |((s - w),(w - t))|)) - (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G)))))) is V11() real ext-real Element of REAL
M - (((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) is V11() real ext-real Element of REAL
M + (- (((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G)))))) is V11() real ext-real set
((Sum (sqr (S - G))) * (M - (((- (2 * |((s - w),(w - t))|)) - (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))))) * (M - (((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G)))))) is V11() real ext-real Element of REAL
(M - (((- (2 * |((s - w),(w - t))|)) - (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G)))))) * (M - (((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G)))))) is V11() real ext-real Element of REAL
(Sum (sqr (S - G))) * ((M - (((- (2 * |((s - w),(w - t))|)) - (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G)))))) * (M - (((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))))) is V11() real ext-real Element of REAL
(((- (2 * |((s - w),(w - t))|)) - (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * (((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) is V11() real ext-real Element of REAL
(((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) ^2 is V11() real ext-real Element of REAL
(((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * (((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) is V11() real ext-real set
(Sum (sqr (S - G))) * ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) ^2) is V11() real ext-real Element of REAL
(2 * |((s - w),(w - t))|) * (((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) is V11() real ext-real Element of REAL
((Sum (sqr (S - G))) * ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) ^2)) + ((2 * |((s - w),(w - t))|) * (((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G)))))) is V11() real ext-real Element of REAL
- ((Sum (sqr (G - T))) - (b ^2)) is V11() real ext-real Element of REAL
(((Sum (sqr (S - G))) * ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) ^2)) + ((2 * |((s - w),(w - t))|) * (((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))))) - (- ((Sum (sqr (G - T))) - (b ^2))) is V11() real ext-real Element of REAL
- (- ((Sum (sqr (G - T))) - (b ^2))) is V11() real ext-real set
(((Sum (sqr (S - G))) * ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) ^2)) + ((2 * |((s - w),(w - t))|) * (((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))))) + (- (- ((Sum (sqr (G - T))) - (b ^2)))) is V11() real ext-real set
Polynom ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)),(((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G)))))) is V11() real ext-real Element of REAL
Quard ((Sum (sqr (S - G))),(((- (2 * |((s - w),(w - t))|)) - (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))),(((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))),(((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G)))))) is V11() real ext-real Element of REAL
(((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) - (((- (2 * |((s - w),(w - t))|)) - (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) is V11() real ext-real Element of REAL
- (((- (2 * |((s - w),(w - t))|)) - (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) is V11() real ext-real set
(((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) + (- (((- (2 * |((s - w),(w - t))|)) - (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G)))))) is V11() real ext-real set
(((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) - (((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) is V11() real ext-real Element of REAL
(((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) + (- (((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G)))))) is V11() real ext-real set
((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) - (((- (2 * |((s - w),(w - t))|)) - (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G)))))) * ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) - (((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G)))))) is V11() real ext-real Element of REAL
(Sum (sqr (S - G))) * (((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) - (((- (2 * |((s - w),(w - t))|)) - (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G)))))) * ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) - (((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))))) is V11() real ext-real Element of REAL
m - t is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K382((TOP-REAL a),m,(- t)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),m,(- t)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
m + (- t) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
m - t is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K419(m,K448(t)) is V16() V21() set
|.(m - t).| is V11() real ext-real non negative Element of REAL
sqr (m - t) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt ((m - t),(m - t)) is V16() V21() set
Sum (sqr (m - t)) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (m - t))) is V11() real ext-real Element of REAL
|.(m - t).| ^2 is V11() real ext-real Element of REAL
|.(m - t).| * |.(m - t).| is V11() real ext-real non negative set
1 * w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
1 * w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(1 * w) - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(- 1) * ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w) is V16() V21() set
K382((TOP-REAL a),(1 * w),(- ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(1 * w),(- ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(1 * w) + (- ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(1 * w) - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K448(((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w)) is V16() V21() complex-yielding set
K419((1 * w),K448(((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w))) is V16() V21() set
((1 * w) - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w)) + ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 * w) - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w)),((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 * w) - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w)) + ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((1 * w) - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w)) + ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s)) - t is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K382((TOP-REAL a),(((1 * w) - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w)) + ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s)),(- t)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(((1 * w) - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w)) + ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s)),(- t)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(((1 * w) - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w)) + ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s)) + (- t) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((1 * w) - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w)) + ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s)) - t is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K419((((1 * w) - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w)) + ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s)),K448(t)) is V16() V21() set
|.((((1 * w) - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w)) + ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s)) - t).| is V11() real ext-real non negative Element of REAL
sqr ((((1 * w) - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w)) + ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s)) - t) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt (((((1 * w) - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w)) + ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s)) - t),((((1 * w) - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w)) + ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s)) - t)) is V16() V21() set
Sum (sqr ((((1 * w) - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w)) + ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s)) - t)) is V11() real ext-real Element of REAL
sqrt (Sum (sqr ((((1 * w) - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w)) + ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s)) - t))) is V11() real ext-real Element of REAL
|.((((1 * w) - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w)) + ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s)) - t).| ^2 is V11() real ext-real Element of REAL
|.((((1 * w) - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w)) + ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s)) - t).| * |.((((1 * w) - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w)) + ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s)) - t).| is V11() real ext-real non negative set
w - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K382((TOP-REAL a),w,(- ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),w,(- ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
w + (- ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
w - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K419(w,K448(((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w))) is V16() V21() set
(w - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w)) + ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(w - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w)),((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(w - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w)) + ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((w - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w)) + ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s)) - t is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K382((TOP-REAL a),((w - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w)) + ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s)),(- t)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((w - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w)) + ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s)),(- t)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((w - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w)) + ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s)) + (- t) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((w - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w)) + ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s)) - t is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K419(((w - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w)) + ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s)),K448(t)) is V16() V21() set
|.(((w - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w)) + ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s)) - t).| is V11() real ext-real non negative Element of REAL
sqr (((w - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w)) + ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s)) - t) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt ((((w - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w)) + ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s)) - t),(((w - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w)) + ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s)) - t)) is V16() V21() set
Sum (sqr (((w - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w)) + ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s)) - t)) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (((w - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w)) + ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s)) - t))) is V11() real ext-real Element of REAL
|.(((w - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w)) + ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s)) - t).| ^2 is V11() real ext-real Element of REAL
|.(((w - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w)) + ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s)) - t).| * |.(((w - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w)) + ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s)) - t).| is V11() real ext-real non negative set
w + ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),w,((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
w + ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(w + ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s)) - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K382((TOP-REAL a),(w + ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s)),(- ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(w + ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s)),(- ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(w + ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s)) + (- ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(w + ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s)) - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K419((w + ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s)),K448(((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w))) is V16() V21() set
((w + ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s)) - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w)) - t is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K382((TOP-REAL a),((w + ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s)) - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w)),(- t)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((w + ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s)) - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w)),(- t)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((w + ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s)) - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w)) + (- t) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((w + ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s)) - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w)) - t is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K419(((w + ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s)) - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w)),K448(t)) is V16() V21() set
|.(((w + ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s)) - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w)) - t).| is V11() real ext-real non negative Element of REAL
sqr (((w + ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s)) - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w)) - t) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt ((((w + ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s)) - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w)) - t),(((w + ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s)) - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w)) - t)) is V16() V21() set
Sum (sqr (((w + ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s)) - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w)) - t)) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (((w + ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s)) - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w)) - t))) is V11() real ext-real Element of REAL
|.(((w + ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s)) - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w)) - t).| ^2 is V11() real ext-real Element of REAL
|.(((w + ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s)) - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w)) - t).| * |.(((w + ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s)) - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w)) - t).| is V11() real ext-real non negative set
((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s) - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K382((TOP-REAL a),((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s),(- ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s),(- ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s) + (- ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s) - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K419(((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s),K448(((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w))) is V16() V21() set
w + (((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s) - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),w,(((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s) - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
w + (((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s) - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(w + (((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s) - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w))) - t is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K382((TOP-REAL a),(w + (((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s) - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w))),(- t)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(w + (((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s) - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w))),(- t)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(w + (((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s) - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w))) + (- t) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(w + (((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s) - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w))) - t is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K419((w + (((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s) - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w))),K448(t)) is V16() V21() set
|.((w + (((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s) - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w))) - t).| is V11() real ext-real non negative Element of REAL
sqr ((w + (((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s) - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w))) - t) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt (((w + (((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s) - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w))) - t),((w + (((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s) - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w))) - t)) is V16() V21() set
Sum (sqr ((w + (((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s) - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w))) - t)) is V11() real ext-real Element of REAL
sqrt (Sum (sqr ((w + (((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s) - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w))) - t))) is V11() real ext-real Element of REAL
|.((w + (((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s) - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w))) - t).| ^2 is V11() real ext-real Element of REAL
|.((w + (((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s) - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w))) - t).| * |.((w + (((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s) - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w))) - t).| is V11() real ext-real non negative set
(w - t) + (((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s) - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(w - t),(((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s) - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(w - t) + (((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s) - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
|.((w - t) + (((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s) - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w))).| is V11() real ext-real non negative Element of REAL
sqr ((w - t) + (((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s) - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w))) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt (((w - t) + (((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s) - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w))),((w - t) + (((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s) - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w)))) is V16() V21() set
Sum (sqr ((w - t) + (((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s) - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w)))) is V11() real ext-real Element of REAL
sqrt (Sum (sqr ((w - t) + (((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s) - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w))))) is V11() real ext-real Element of REAL
|.((w - t) + (((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s) - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w))).| ^2 is V11() real ext-real Element of REAL
|.((w - t) + (((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s) - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w))).| * |.((w - t) + (((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s) - ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * w))).| is V11() real ext-real non negative set
(((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * (s - w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * (s - w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(w - t) + ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * (s - w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(w - t),((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * (s - w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(w - t) + ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * (s - w)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
|.((w - t) + ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * (s - w))).| is V11() real ext-real non negative Element of REAL
sqr ((w - t) + ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * (s - w))) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt (((w - t) + ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * (s - w))),((w - t) + ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * (s - w)))) is V16() V21() set
Sum (sqr ((w - t) + ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * (s - w)))) is V11() real ext-real Element of REAL
sqrt (Sum (sqr ((w - t) + ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * (s - w))))) is V11() real ext-real Element of REAL
|.((w - t) + ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * (s - w))).| ^2 is V11() real ext-real Element of REAL
|.((w - t) + ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * (s - w))).| * |.((w - t) + ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * (s - w))).| is V11() real ext-real non negative set
|.(w - t).| ^2 is V11() real ext-real Element of REAL
|.(w - t).| * |.(w - t).| is V11() real ext-real non negative set
|(((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * (s - w)),(w - t))| is V11() real ext-real Element of REAL
2 * |(((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * (s - w)),(w - t))| is V11() real ext-real Element of REAL
(|.(w - t).| ^2) + (2 * |(((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * (s - w)),(w - t))|) is V11() real ext-real Element of REAL
|.((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * (s - w)).| is V11() real ext-real non negative Element of REAL
sqr ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * (s - w)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt (((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * (s - w)),((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * (s - w))) is V16() V21() set
Sum (sqr ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * (s - w))) is V11() real ext-real Element of REAL
sqrt (Sum (sqr ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * (s - w)))) is V11() real ext-real Element of REAL
|.((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * (s - w)).| ^2 is V11() real ext-real Element of REAL
|.((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * (s - w)).| * |.((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * (s - w)).| is V11() real ext-real non negative set
((|.(w - t).| ^2) + (2 * |(((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * (s - w)),(w - t))|)) + (|.((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * (s - w)).| ^2) is V11() real ext-real Element of REAL
(((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * |((s - w),(w - t))| is V11() real ext-real Element of REAL
2 * ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * |((s - w),(w - t))|) is V11() real ext-real Element of REAL
(Sum (sqr (G - T))) + (2 * ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * |((s - w),(w - t))|)) is V11() real ext-real Element of REAL
((Sum (sqr (G - T))) + (2 * ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * |((s - w),(w - t))|))) + (|.((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * (s - w)).| ^2) is V11() real ext-real Element of REAL
2 * (((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) is V11() real ext-real Element of REAL
(2 * (((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G)))))) * |((s - w),(w - t))| is V11() real ext-real Element of REAL
(Sum (sqr (G - T))) + ((2 * (((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G)))))) * |((s - w),(w - t))|) is V11() real ext-real Element of REAL
abs (((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) is V11() real ext-real Element of REAL
|.(s - w).| is V11() real ext-real non negative Element of REAL
sqr (s - w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt ((s - w),(s - w)) is V16() V21() set
Sum (sqr (s - w)) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (s - w))) is V11() real ext-real Element of REAL
(abs (((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G)))))) * |.(s - w).| is V11() real ext-real Element of REAL
((abs (((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G)))))) * |.(s - w).|) ^2 is V11() real ext-real Element of REAL
((abs (((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G)))))) * |.(s - w).|) * ((abs (((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G)))))) * |.(s - w).|) is V11() real ext-real set
((Sum (sqr (G - T))) + ((2 * (((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G)))))) * |((s - w),(w - t))|)) + (((abs (((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G)))))) * |.(s - w).|) ^2) is V11() real ext-real Element of REAL
(abs (((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G)))))) ^2 is V11() real ext-real Element of REAL
(abs (((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G)))))) * (abs (((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G)))))) is V11() real ext-real set
|.(s - w).| ^2 is V11() real ext-real Element of REAL
|.(s - w).| * |.(s - w).| is V11() real ext-real non negative set
((abs (((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G)))))) ^2) * (|.(s - w).| ^2) is V11() real ext-real Element of REAL
((Sum (sqr (G - T))) + ((2 * (((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G)))))) * |((s - w),(w - t))|)) + (((abs (((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G)))))) ^2) * (|.(s - w).| ^2)) is V11() real ext-real Element of REAL
(((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * (2 * |((s - w),(w - t))|) is V11() real ext-real Element of REAL
(Sum (sqr (G - T))) + ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * (2 * |((s - w),(w - t))|)) is V11() real ext-real Element of REAL
((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) ^2) * (|.(S - G).| ^2) is V11() real ext-real Element of REAL
((Sum (sqr (G - T))) + ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * (2 * |((s - w),(w - t))|))) + (((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) ^2) * (|.(S - G).| ^2)) is V11() real ext-real Element of REAL
((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) ^2) * (Sum (sqr (S - G))) is V11() real ext-real Element of REAL
((Sum (sqr (G - T))) + ((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * (2 * |((s - w),(w - t))|))) + (((((- (2 * |((s - w),(w - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) ^2) * (Sum (sqr (S - G)))) is V11() real ext-real Element of REAL
M is set
M is set
o is V11() real ext-real set
1 - o is V11() real ext-real Element of REAL
- o is V11() real ext-real set
1 + (- o) is V11() real ext-real set
(1 - o) * w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(1 - o) * w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
o * s is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
o * s is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - o) * w) + (o * s) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 - o) * w),(o * s)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - o) * w) + (o * s) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
o * (s - w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
o * (s - w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
|.(o * (s - w)).| is V11() real ext-real non negative Element of REAL
sqr (o * (s - w)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt ((o * (s - w)),(o * (s - w))) is V16() V21() set
Sum (sqr (o * (s - w))) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (o * (s - w)))) is V11() real ext-real Element of REAL
|.(o * (s - w)).| ^2 is V11() real ext-real Element of REAL
|.(o * (s - w)).| * |.(o * (s - w)).| is V11() real ext-real non negative set
abs o is V11() real ext-real Element of REAL
(abs o) * |.(s - w).| is V11() real ext-real Element of REAL
((abs o) * |.(s - w).|) ^2 is V11() real ext-real Element of REAL
((abs o) * |.(s - w).|) * ((abs o) * |.(s - w).|) is V11() real ext-real set
(abs o) ^2 is V11() real ext-real Element of REAL
(abs o) * (abs o) is V11() real ext-real set
((abs o) ^2) * (|.(s - w).| ^2) is V11() real ext-real Element of REAL
o ^2 is V11() real ext-real set
o * o is V11() real ext-real set
(o ^2) * (|.(s - w).| ^2) is V11() real ext-real Element of REAL
(((1 - o) * w) + (o * s)) - t is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K382((TOP-REAL a),(((1 - o) * w) + (o * s)),(- t)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(((1 - o) * w) + (o * s)),(- t)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(((1 - o) * w) + (o * s)) + (- t) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((1 - o) * w) + (o * s)) - t is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K419((((1 - o) * w) + (o * s)),K448(t)) is V16() V21() set
|.((((1 - o) * w) + (o * s)) - t).| is V11() real ext-real non negative Element of REAL
sqr ((((1 - o) * w) + (o * s)) - t) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt (((((1 - o) * w) + (o * s)) - t),((((1 - o) * w) + (o * s)) - t)) is V16() V21() set
Sum (sqr ((((1 - o) * w) + (o * s)) - t)) is V11() real ext-real Element of REAL
sqrt (Sum (sqr ((((1 - o) * w) + (o * s)) - t))) is V11() real ext-real Element of REAL
o * w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
o * w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(1 * w) - (o * w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- (o * w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- (o * w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(- 1) * (o * w) is V16() V21() set
K382((TOP-REAL a),(1 * w),(- (o * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(1 * w),(- (o * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(1 * w) + (- (o * w)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(1 * w) - (o * w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K448((o * w)) is V16() V21() complex-yielding set
K419((1 * w),K448((o * w))) is V16() V21() set
((1 * w) - (o * w)) + (o * s) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 * w) - (o * w)),(o * s)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 * w) - (o * w)) + (o * s) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((1 * w) - (o * w)) + (o * s)) - t is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K382((TOP-REAL a),(((1 * w) - (o * w)) + (o * s)),(- t)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(((1 * w) - (o * w)) + (o * s)),(- t)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(((1 * w) - (o * w)) + (o * s)) + (- t) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((1 * w) - (o * w)) + (o * s)) - t is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K419((((1 * w) - (o * w)) + (o * s)),K448(t)) is V16() V21() set
|.((((1 * w) - (o * w)) + (o * s)) - t).| is V11() real ext-real non negative Element of REAL
sqr ((((1 * w) - (o * w)) + (o * s)) - t) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt (((((1 * w) - (o * w)) + (o * s)) - t),((((1 * w) - (o * w)) + (o * s)) - t)) is V16() V21() set
Sum (sqr ((((1 * w) - (o * w)) + (o * s)) - t)) is V11() real ext-real Element of REAL
sqrt (Sum (sqr ((((1 * w) - (o * w)) + (o * s)) - t))) is V11() real ext-real Element of REAL
w - (o * w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K382((TOP-REAL a),w,(- (o * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),w,(- (o * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
w + (- (o * w)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
w - (o * w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K419(w,K448((o * w))) is V16() V21() set
(w - (o * w)) + (o * s) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(w - (o * w)),(o * s)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(w - (o * w)) + (o * s) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((w - (o * w)) + (o * s)) - t is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K382((TOP-REAL a),((w - (o * w)) + (o * s)),(- t)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((w - (o * w)) + (o * s)),(- t)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((w - (o * w)) + (o * s)) + (- t) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((w - (o * w)) + (o * s)) - t is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K419(((w - (o * w)) + (o * s)),K448(t)) is V16() V21() set
|.(((w - (o * w)) + (o * s)) - t).| is V11() real ext-real non negative Element of REAL
sqr (((w - (o * w)) + (o * s)) - t) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt ((((w - (o * w)) + (o * s)) - t),(((w - (o * w)) + (o * s)) - t)) is V16() V21() set
Sum (sqr (((w - (o * w)) + (o * s)) - t)) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (((w - (o * w)) + (o * s)) - t))) is V11() real ext-real Element of REAL
(o * w) - (o * s) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- (o * s) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- (o * s) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(- 1) * (o * s) is V16() V21() set
K382((TOP-REAL a),(o * w),(- (o * s))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(o * w),(- (o * s))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(o * w) + (- (o * s)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(o * w) - (o * s) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K448((o * s)) is V16() V21() complex-yielding set
K419((o * w),K448((o * s))) is V16() V21() set
w - ((o * w) - (o * s)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- ((o * w) - (o * s)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- ((o * w) - (o * s)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(- 1) * ((o * w) - (o * s)) is V16() V21() set
K382((TOP-REAL a),w,(- ((o * w) - (o * s)))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),w,(- ((o * w) - (o * s)))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
w + (- ((o * w) - (o * s))) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
w - ((o * w) - (o * s)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K448(((o * w) - (o * s))) is V16() V21() complex-yielding set
K419(w,K448(((o * w) - (o * s)))) is V16() V21() set
(w - ((o * w) - (o * s))) - t is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K382((TOP-REAL a),(w - ((o * w) - (o * s))),(- t)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(w - ((o * w) - (o * s))),(- t)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(w - ((o * w) - (o * s))) + (- t) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(w - ((o * w) - (o * s))) - t is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K419((w - ((o * w) - (o * s))),K448(t)) is V16() V21() set
|.((w - ((o * w) - (o * s))) - t).| is V11() real ext-real non negative Element of REAL
sqr ((w - ((o * w) - (o * s))) - t) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt (((w - ((o * w) - (o * s))) - t),((w - ((o * w) - (o * s))) - t)) is V16() V21() set
Sum (sqr ((w - ((o * w) - (o * s))) - t)) is V11() real ext-real Element of REAL
sqrt (Sum (sqr ((w - ((o * w) - (o * s))) - t))) is V11() real ext-real Element of REAL
w + (- ((o * w) - (o * s))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(w + (- ((o * w) - (o * s)))) + (- t) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(w + (- ((o * w) - (o * s)))),(- t)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(w + (- ((o * w) - (o * s)))) + (- t) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
|.((w + (- ((o * w) - (o * s)))) + (- t)).| is V11() real ext-real non negative Element of REAL
sqr ((w + (- ((o * w) - (o * s)))) + (- t)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt (((w + (- ((o * w) - (o * s)))) + (- t)),((w + (- ((o * w) - (o * s)))) + (- t))) is V16() V21() set
Sum (sqr ((w + (- ((o * w) - (o * s)))) + (- t))) is V11() real ext-real Element of REAL
sqrt (Sum (sqr ((w + (- ((o * w) - (o * s)))) + (- t)))) is V11() real ext-real Element of REAL
w + (- t) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(w + (- t)) + (- ((o * w) - (o * s))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(w + (- t)),(- ((o * w) - (o * s)))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(w + (- t)) + (- ((o * w) - (o * s))) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
|.((w + (- t)) + (- ((o * w) - (o * s)))).| is V11() real ext-real non negative Element of REAL
sqr ((w + (- t)) + (- ((o * w) - (o * s)))) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt (((w + (- t)) + (- ((o * w) - (o * s)))),((w + (- t)) + (- ((o * w) - (o * s))))) is V16() V21() set
Sum (sqr ((w + (- t)) + (- ((o * w) - (o * s))))) is V11() real ext-real Element of REAL
sqrt (Sum (sqr ((w + (- t)) + (- ((o * w) - (o * s)))))) is V11() real ext-real Element of REAL
(w - t) - ((o * w) - (o * s)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K382((TOP-REAL a),(w - t),(- ((o * w) - (o * s)))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(w - t),(- ((o * w) - (o * s)))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(w - t) + (- ((o * w) - (o * s))) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(w - t) - ((o * w) - (o * s)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K419((w - t),K448(((o * w) - (o * s)))) is V16() V21() set
|.((w - t) - ((o * w) - (o * s))).| is V11() real ext-real non negative Element of REAL
sqr ((w - t) - ((o * w) - (o * s))) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt (((w - t) - ((o * w) - (o * s))),((w - t) - ((o * w) - (o * s)))) is V16() V21() set
Sum (sqr ((w - t) - ((o * w) - (o * s)))) is V11() real ext-real Element of REAL
sqrt (Sum (sqr ((w - t) - ((o * w) - (o * s))))) is V11() real ext-real Element of REAL
w - s is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- s is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- s is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(- 1) * s is V16() V21() set
K382((TOP-REAL a),w,(- s)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),w,(- s)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
w + (- s) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
w - s is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K448(s) is V16() V21() complex-yielding set
K419(w,K448(s)) is V16() V21() set
o * (w - s) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
o * (w - s) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
- (o * (w - s)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- (o * (w - s)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(- 1) * (o * (w - s)) is V16() V21() set
(w - t) + (- (o * (w - s))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(w - t),(- (o * (w - s)))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(w - t) + (- (o * (w - s))) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
|.((w - t) + (- (o * (w - s)))).| is V11() real ext-real non negative Element of REAL
sqr ((w - t) + (- (o * (w - s)))) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt (((w - t) + (- (o * (w - s)))),((w - t) + (- (o * (w - s))))) is V16() V21() set
Sum (sqr ((w - t) + (- (o * (w - s))))) is V11() real ext-real Element of REAL
sqrt (Sum (sqr ((w - t) + (- (o * (w - s)))))) is V11() real ext-real Element of REAL
- (w - s) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- (w - s) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(- 1) * (w - s) is V16() V21() set
o * (- (w - s)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
o * (- (w - s)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(w - t) + (o * (- (w - s))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(w - t),(o * (- (w - s)))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(w - t) + (o * (- (w - s))) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
|.((w - t) + (o * (- (w - s)))).| is V11() real ext-real non negative Element of REAL
sqr ((w - t) + (o * (- (w - s)))) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt (((w - t) + (o * (- (w - s)))),((w - t) + (o * (- (w - s))))) is V16() V21() set
Sum (sqr ((w - t) + (o * (- (w - s))))) is V11() real ext-real Element of REAL
sqrt (Sum (sqr ((w - t) + (o * (- (w - s)))))) is V11() real ext-real Element of REAL
(w - t) + (o * (s - w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(w - t),(o * (s - w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(w - t) + (o * (s - w)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
|.((w - t) + (o * (s - w))).| is V11() real ext-real non negative Element of REAL
sqr ((w - t) + (o * (s - w))) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt (((w - t) + (o * (s - w))),((w - t) + (o * (s - w)))) is V16() V21() set
Sum (sqr ((w - t) + (o * (s - w)))) is V11() real ext-real Element of REAL
sqrt (Sum (sqr ((w - t) + (o * (s - w))))) is V11() real ext-real Element of REAL
|((o * (s - w)),(w - t))| is V11() real ext-real Element of REAL
2 * |((o * (s - w)),(w - t))| is V11() real ext-real Element of REAL
(|.(w - t).| ^2) + (2 * |((o * (s - w)),(w - t))|) is V11() real ext-real Element of REAL
((|.(w - t).| ^2) + (2 * |((o * (s - w)),(w - t))|)) + (|.(o * (s - w)).| ^2) is V11() real ext-real Element of REAL
o * |((s - w),(w - t))| is V11() real ext-real Element of REAL
2 * (o * |((s - w),(w - t))|) is V11() real ext-real Element of REAL
(|.(w - t).| ^2) + (2 * (o * |((s - w),(w - t))|)) is V11() real ext-real Element of REAL
((|.(w - t).| ^2) + (2 * (o * |((s - w),(w - t))|))) + (|.(o * (s - w)).| ^2) is V11() real ext-real Element of REAL
(Sum (sqr (S - G))) * (o ^2) is V11() real ext-real Element of REAL
(2 * |((s - w),(w - t))|) * o is V11() real ext-real Element of REAL
((Sum (sqr (S - G))) * (o ^2)) + ((2 * |((s - w),(w - t))|) * o) is V11() real ext-real Element of REAL
(((Sum (sqr (S - G))) * (o ^2)) + ((2 * |((s - w),(w - t))|) * o)) + ((Sum (sqr (G - T))) - (b ^2)) is V11() real ext-real Element of REAL
Polynom ((Sum (sqr (S - G))),(2 * |((s - w),(w - t))|),((Sum (sqr (G - T))) - (b ^2)),o) is set
1 / 2 is V11() real ext-real non negative Element of REAL
2 " is non empty V11() real ext-real positive non negative set
1 * (2 ") is V11() real ext-real non negative set
a is ordinal natural V11() real ext-real non negative V33() V34() V179() V180() V181() V182() V183() V184() Element of NAT
TOP-REAL a is non empty TopSpace-like V126() V191() V192() V209() V210() V211() V212() V213() V214() V215() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL a) is non empty set
REAL a is non empty V24() FinSequence-membered FinSequenceSet of REAL
a -tuples_on REAL is V24() FinSequence-membered FinSequenceSet of REAL
b is V11() real ext-real set
b ^2 is V11() real ext-real set
b * b is V11() real ext-real set
r is V11() real ext-real set
1 - r is V11() real ext-real Element of REAL
- r is V11() real ext-real set
1 + (- r) is V11() real ext-real set
w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(1 / 2) * w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(1 / 2) * w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
s is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(1 / 2) * s is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(1 / 2) * s is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 / 2) * w) + ((1 / 2) * s) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
the U7 of (TOP-REAL a) is V16() V21() V30(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) Element of K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)))
K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)) is V16() set
K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) is V16() set
K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a))) is set
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 / 2) * w),((1 / 2) * s)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 / 2) * w) + ((1 / 2) * s) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(a,w,s) is non empty convex Element of K6( the carrier of (TOP-REAL a))
K6( the carrier of (TOP-REAL a)) is set
{ (((1 - b1) * w) + (b1 * s)) where b1 is V11() real ext-real Element of REAL : 0 <= b1 } is set
s - (((1 / 2) * w) + ((1 / 2) * s)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- (((1 / 2) * w) + ((1 / 2) * s)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- (((1 / 2) * w) + ((1 / 2) * s)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
- 1 is V11() real ext-real non positive set
(- 1) * (((1 / 2) * w) + ((1 / 2) * s)) is V16() V21() set
K382((TOP-REAL a),s,(- (((1 / 2) * w) + ((1 / 2) * s)))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),s,(- (((1 / 2) * w) + ((1 / 2) * s)))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
s + (- (((1 / 2) * w) + ((1 / 2) * s))) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
s - (((1 / 2) * w) + ((1 / 2) * s)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K448((((1 / 2) * w) + ((1 / 2) * s))) is V16() V21() complex-yielding set
K419(s,K448((((1 / 2) * w) + ((1 / 2) * s)))) is V16() V21() set
(1 - r) * (((1 / 2) * w) + ((1 / 2) * s)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(1 - r) * (((1 / 2) * w) + ((1 / 2) * s)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
r * s is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
r * s is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - r) * (((1 / 2) * w) + ((1 / 2) * s))) + (r * s) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 - r) * (((1 / 2) * w) + ((1 / 2) * s))),(r * s)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - r) * (((1 / 2) * w) + ((1 / 2) * s))) + (r * s) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
t is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(a,t,b) is closed bounded Element of K6( the carrier of (TOP-REAL a))
{ b1 where b1 is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a) : |.(b1 - t).| = b } is set
(a,t,b) is closed bounded convex Element of K6( the carrier of (TOP-REAL a))
{ b1 where b1 is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a) : |.(b1 - t).| <= b } is set
(a,w,s) /\ (a,t,b) is Element of K6( the carrier of (TOP-REAL a))
(((1 / 2) * w) + ((1 / 2) * s)) - t is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- t is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- t is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(- 1) * t is V16() V21() set
K382((TOP-REAL a),(((1 / 2) * w) + ((1 / 2) * s)),(- t)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(((1 / 2) * w) + ((1 / 2) * s)),(- t)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(((1 / 2) * w) + ((1 / 2) * s)) + (- t) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((1 / 2) * w) + ((1 / 2) * s)) - t is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K448(t) is V16() V21() complex-yielding set
K419((((1 / 2) * w) + ((1 / 2) * s)),K448(t)) is V16() V21() set
|((s - (((1 / 2) * w) + ((1 / 2) * s))),((((1 / 2) * w) + ((1 / 2) * s)) - t))| is V11() real ext-real Element of REAL
2 * |((s - (((1 / 2) * w) + ((1 / 2) * s))),((((1 / 2) * w) + ((1 / 2) * s)) - t))| is V11() real ext-real Element of REAL
- (2 * |((s - (((1 / 2) * w) + ((1 / 2) * s))),((((1 / 2) * w) + ((1 / 2) * s)) - t))|) is V11() real ext-real Element of REAL
G is V16() V19( NAT ) V20( REAL ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL a
S is V16() V19( NAT ) V20( REAL ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL a
T is V16() V19( NAT ) V20( REAL ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL a
S - G is V16() V19( NAT ) V20( REAL ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL a
K448(G) is V16() V21() complex-yielding set
(- 1) * G is V16() V21() set
K419(S,K448(G)) is V16() V21() set
sqr (S - G) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of a -tuples_on REAL
mlt ((S - G),(S - G)) is V16() V21() set
Sum (sqr (S - G)) is V11() real ext-real Element of REAL
G - T is V16() V19( NAT ) V20( REAL ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL a
K448(T) is V16() V21() complex-yielding set
(- 1) * T is V16() V21() set
K419(G,K448(T)) is V16() V21() set
sqr (G - T) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of a -tuples_on REAL
mlt ((G - T),(G - T)) is V16() V21() set
Sum (sqr (G - T)) is V11() real ext-real Element of REAL
(Sum (sqr (G - T))) - (b ^2) is V11() real ext-real Element of REAL
- (b ^2) is V11() real ext-real set
(Sum (sqr (G - T))) + (- (b ^2)) is V11() real ext-real set
delta ((Sum (sqr (S - G))),(2 * |((s - (((1 / 2) * w) + ((1 / 2) * s))),((((1 / 2) * w) + ((1 / 2) * s)) - t))|),((Sum (sqr (G - T))) - (b ^2))) is V11() real ext-real Element of REAL
sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - (((1 / 2) * w) + ((1 / 2) * s))),((((1 / 2) * w) + ((1 / 2) * s)) - t))|),((Sum (sqr (G - T))) - (b ^2)))) is V11() real ext-real Element of REAL
(- (2 * |((s - (((1 / 2) * w) + ((1 / 2) * s))),((((1 / 2) * w) + ((1 / 2) * s)) - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - (((1 / 2) * w) + ((1 / 2) * s))),((((1 / 2) * w) + ((1 / 2) * s)) - t))|),((Sum (sqr (G - T))) - (b ^2))))) is V11() real ext-real Element of REAL
2 * (Sum (sqr (S - G))) is V11() real ext-real Element of REAL
((- (2 * |((s - (((1 / 2) * w) + ((1 / 2) * s))),((((1 / 2) * w) + ((1 / 2) * s)) - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - (((1 / 2) * w) + ((1 / 2) * s))),((((1 / 2) * w) + ((1 / 2) * s)) - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G)))) is V11() real ext-real Element of REAL
(2 * (Sum (sqr (S - G)))) " is V11() real ext-real set
((- (2 * |((s - (((1 / 2) * w) + ((1 / 2) * s))),((((1 / 2) * w) + ((1 / 2) * s)) - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - (((1 / 2) * w) + ((1 / 2) * s))),((((1 / 2) * w) + ((1 / 2) * s)) - t))|),((Sum (sqr (G - T))) - (b ^2)))))) * ((2 * (Sum (sqr (S - G)))) ") is V11() real ext-real set
Euclid a is non empty strict Reflexive discerning V103() triangle MetrStruct
Pitag_dist a is V16() V21() V30(K7((REAL a),(REAL a)), REAL ) complex-yielding ext-real-valued real-valued Element of K6(K7(K7((REAL a),(REAL a)),REAL))
K7((REAL a),(REAL a)) is V16() set
K7(K7((REAL a),(REAL a)),REAL) is V16() complex-yielding ext-real-valued real-valued set
K6(K7(K7((REAL a),(REAL a)),REAL)) is set
MetrStruct(# (REAL a),(Pitag_dist a) #) is strict MetrStruct
the carrier of (Euclid a) is non empty set
Y is Element of the carrier of (Euclid a)
Ball (Y,b) is bounded Element of K6( the carrier of (Euclid a))
K6( the carrier of (Euclid a)) is set
(a,t,b) is open bounded convex Element of K6( the carrier of (TOP-REAL a))
{ b1 where b1 is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a) : not b <= |.(b1 - t).| } is set
{w,s} is non empty V24() set
- ((1 / 2) * w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- ((1 / 2) * w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(- 1) * ((1 / 2) * w) is V16() V21() set
s + (- ((1 / 2) * w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),s,(- ((1 / 2) * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
s + (- ((1 / 2) * w)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
- ((1 / 2) * s) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- ((1 / 2) * s) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(- 1) * ((1 / 2) * s) is V16() V21() set
(s + (- ((1 / 2) * w))) + (- ((1 / 2) * s)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(s + (- ((1 / 2) * w))),(- ((1 / 2) * s))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(s + (- ((1 / 2) * w))) + (- ((1 / 2) * s)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
s - ((1 / 2) * w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K382((TOP-REAL a),s,(- ((1 / 2) * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
s - ((1 / 2) * w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K448(((1 / 2) * w)) is V16() V21() complex-yielding set
K419(s,K448(((1 / 2) * w))) is V16() V21() set
(s - ((1 / 2) * w)) - ((1 / 2) * s) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K382((TOP-REAL a),(s - ((1 / 2) * w)),(- ((1 / 2) * s))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(s - ((1 / 2) * w)),(- ((1 / 2) * s))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(s - ((1 / 2) * w)) + (- ((1 / 2) * s)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(s - ((1 / 2) * w)) - ((1 / 2) * s) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K448(((1 / 2) * s)) is V16() V21() complex-yielding set
K419((s - ((1 / 2) * w)),K448(((1 / 2) * s))) is V16() V21() set
s - s is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- s is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- s is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(- 1) * s is V16() V21() set
K382((TOP-REAL a),s,(- s)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),s,(- s)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
s + (- s) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
s - s is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K448(s) is V16() V21() complex-yielding set
K419(s,K448(s)) is V16() V21() set
0. (TOP-REAL a) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like V69( TOP-REAL a) complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
the ZeroF of (TOP-REAL a) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
s + (- ((1 / 2) * s)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),s,(- ((1 / 2) * s))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
s + (- ((1 / 2) * s)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(s + (- ((1 / 2) * s))) + (- ((1 / 2) * w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(s + (- ((1 / 2) * s))),(- ((1 / 2) * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(s + (- ((1 / 2) * s))) + (- ((1 / 2) * w)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
1 * s is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
1 * s is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(1 * s) - ((1 / 2) * s) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K382((TOP-REAL a),(1 * s),(- ((1 / 2) * s))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(1 * s),(- ((1 / 2) * s))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(1 * s) + (- ((1 / 2) * s)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(1 * s) - ((1 / 2) * s) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K419((1 * s),K448(((1 / 2) * s))) is V16() V21() set
((1 * s) - ((1 / 2) * s)) - ((1 / 2) * w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K382((TOP-REAL a),((1 * s) - ((1 / 2) * s)),(- ((1 / 2) * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 * s) - ((1 / 2) * s)),(- ((1 / 2) * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 * s) - ((1 / 2) * s)) + (- ((1 / 2) * w)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 * s) - ((1 / 2) * s)) - ((1 / 2) * w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K419(((1 * s) - ((1 / 2) * s)),K448(((1 / 2) * w))) is V16() V21() set
1 - (1 / 2) is V11() real ext-real Element of REAL
- (1 / 2) is V11() real ext-real non positive set
1 + (- (1 / 2)) is V11() real ext-real set
(1 - (1 / 2)) * s is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(1 - (1 / 2)) * s is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - (1 / 2)) * s) - ((1 / 2) * w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K382((TOP-REAL a),((1 - (1 / 2)) * s),(- ((1 / 2) * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 - (1 / 2)) * s),(- ((1 / 2) * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - (1 / 2)) * s) + (- ((1 / 2) * w)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - (1 / 2)) * s) - ((1 / 2) * w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K419(((1 - (1 / 2)) * s),K448(((1 / 2) * w))) is V16() V21() set
s - w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(- 1) * w is V16() V21() set
K382((TOP-REAL a),s,(- w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),s,(- w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
s + (- w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
s - w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K448(w) is V16() V21() complex-yielding set
K419(s,K448(w)) is V16() V21() set
(1 / 2) * (s - w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(1 / 2) * (s - w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(a,t,b) \/ (a,t,b) is Element of K6( the carrier of (TOP-REAL a))
(1 / 2) + (1 / 2) is V11() real ext-real non negative Element of REAL
abs (1 / 2) is V11() real ext-real Element of REAL
(a,(((1 / 2) * w) + ((1 / 2) * s)),s) is non empty convex Element of K6( the carrier of (TOP-REAL a))
{ (((1 - b1) * (((1 / 2) * w) + ((1 / 2) * s))) + (b1 * s)) where b1 is V11() real ext-real Element of REAL : 0 <= b1 } is set
(a,(((1 / 2) * w) + ((1 / 2) * s)),s) /\ (a,t,b) is Element of K6( the carrier of (TOP-REAL a))
1 - (((- (2 * |((s - (((1 / 2) * w) + ((1 / 2) * s))),((((1 / 2) * w) + ((1 / 2) * s)) - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - (((1 / 2) * w) + ((1 / 2) * s))),((((1 / 2) * w) + ((1 / 2) * s)) - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) is V11() real ext-real Element of REAL
- (((- (2 * |((s - (((1 / 2) * w) + ((1 / 2) * s))),((((1 / 2) * w) + ((1 / 2) * s)) - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - (((1 / 2) * w) + ((1 / 2) * s))),((((1 / 2) * w) + ((1 / 2) * s)) - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) is V11() real ext-real set
1 + (- (((- (2 * |((s - (((1 / 2) * w) + ((1 / 2) * s))),((((1 / 2) * w) + ((1 / 2) * s)) - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - (((1 / 2) * w) + ((1 / 2) * s))),((((1 / 2) * w) + ((1 / 2) * s)) - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G)))))) is V11() real ext-real set
(1 - (((- (2 * |((s - (((1 / 2) * w) + ((1 / 2) * s))),((((1 / 2) * w) + ((1 / 2) * s)) - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - (((1 / 2) * w) + ((1 / 2) * s))),((((1 / 2) * w) + ((1 / 2) * s)) - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G)))))) * (((1 / 2) * w) + ((1 / 2) * s)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(1 - (((- (2 * |((s - (((1 / 2) * w) + ((1 / 2) * s))),((((1 / 2) * w) + ((1 / 2) * s)) - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - (((1 / 2) * w) + ((1 / 2) * s))),((((1 / 2) * w) + ((1 / 2) * s)) - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G)))))) * (((1 / 2) * w) + ((1 / 2) * s)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((- (2 * |((s - (((1 / 2) * w) + ((1 / 2) * s))),((((1 / 2) * w) + ((1 / 2) * s)) - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - (((1 / 2) * w) + ((1 / 2) * s))),((((1 / 2) * w) + ((1 / 2) * s)) - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(((- (2 * |((s - (((1 / 2) * w) + ((1 / 2) * s))),((((1 / 2) * w) + ((1 / 2) * s)) - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - (((1 / 2) * w) + ((1 / 2) * s))),((((1 / 2) * w) + ((1 / 2) * s)) - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - (((- (2 * |((s - (((1 / 2) * w) + ((1 / 2) * s))),((((1 / 2) * w) + ((1 / 2) * s)) - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - (((1 / 2) * w) + ((1 / 2) * s))),((((1 / 2) * w) + ((1 / 2) * s)) - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G)))))) * (((1 / 2) * w) + ((1 / 2) * s))) + ((((- (2 * |((s - (((1 / 2) * w) + ((1 / 2) * s))),((((1 / 2) * w) + ((1 / 2) * s)) - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - (((1 / 2) * w) + ((1 / 2) * s))),((((1 / 2) * w) + ((1 / 2) * s)) - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 - (((- (2 * |((s - (((1 / 2) * w) + ((1 / 2) * s))),((((1 / 2) * w) + ((1 / 2) * s)) - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - (((1 / 2) * w) + ((1 / 2) * s))),((((1 / 2) * w) + ((1 / 2) * s)) - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G)))))) * (((1 / 2) * w) + ((1 / 2) * s))),((((- (2 * |((s - (((1 / 2) * w) + ((1 / 2) * s))),((((1 / 2) * w) + ((1 / 2) * s)) - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - (((1 / 2) * w) + ((1 / 2) * s))),((((1 / 2) * w) + ((1 / 2) * s)) - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - (((- (2 * |((s - (((1 / 2) * w) + ((1 / 2) * s))),((((1 / 2) * w) + ((1 / 2) * s)) - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - (((1 / 2) * w) + ((1 / 2) * s))),((((1 / 2) * w) + ((1 / 2) * s)) - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G)))))) * (((1 / 2) * w) + ((1 / 2) * s))) + ((((- (2 * |((s - (((1 / 2) * w) + ((1 / 2) * s))),((((1 / 2) * w) + ((1 / 2) * s)) - t))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((s - (((1 / 2) * w) + ((1 / 2) * s))),((((1 / 2) * w) + ((1 / 2) * s)) - t))|),((Sum (sqr (G - T))) - (b ^2)))))) / (2 * (Sum (sqr (S - G))))) * s) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
e1 is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
{e1} is non empty V24() set
{w,e1} is non empty V24() set
l is V11() real ext-real set
1 - l is V11() real ext-real Element of REAL
- l is V11() real ext-real set
1 + (- l) is V11() real ext-real set
(1 - l) * (((1 / 2) * w) + ((1 / 2) * s)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(1 - l) * (((1 / 2) * w) + ((1 / 2) * s)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
l * s is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
l * s is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - l) * (((1 / 2) * w) + ((1 / 2) * s))) + (l * s) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 - l) * (((1 / 2) * w) + ((1 / 2) * s))),(l * s)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - l) * (((1 / 2) * w) + ((1 / 2) * s))) + (l * s) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((1 - l) * (((1 / 2) * w) + ((1 / 2) * s))) + (l * s)) - w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K382((TOP-REAL a),(((1 - l) * (((1 / 2) * w) + ((1 / 2) * s))) + (l * s)),(- w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(((1 - l) * (((1 / 2) * w) + ((1 / 2) * s))) + (l * s)),(- w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(((1 - l) * (((1 / 2) * w) + ((1 / 2) * s))) + (l * s)) + (- w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((1 - l) * (((1 / 2) * w) + ((1 / 2) * s))) + (l * s)) - w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K419((((1 - l) * (((1 / 2) * w) + ((1 / 2) * s))) + (l * s)),K448(w)) is V16() V21() set
(1 - l) * ((1 / 2) * w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(1 - l) * ((1 / 2) * w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(1 - l) * ((1 / 2) * s) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(1 - l) * ((1 / 2) * s) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - l) * ((1 / 2) * w)) + ((1 - l) * ((1 / 2) * s)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 - l) * ((1 / 2) * w)),((1 - l) * ((1 / 2) * s))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - l) * ((1 / 2) * w)) + ((1 - l) * ((1 / 2) * s)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((1 - l) * ((1 / 2) * w)) + ((1 - l) * ((1 / 2) * s))) + (l * s) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(((1 - l) * ((1 / 2) * w)) + ((1 - l) * ((1 / 2) * s))),(l * s)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(((1 - l) * ((1 / 2) * w)) + ((1 - l) * ((1 / 2) * s))) + (l * s) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((((1 - l) * ((1 / 2) * w)) + ((1 - l) * ((1 / 2) * s))) + (l * s)) - w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K382((TOP-REAL a),((((1 - l) * ((1 / 2) * w)) + ((1 - l) * ((1 / 2) * s))) + (l * s)),(- w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((((1 - l) * ((1 / 2) * w)) + ((1 - l) * ((1 / 2) * s))) + (l * s)),(- w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((((1 - l) * ((1 / 2) * w)) + ((1 - l) * ((1 / 2) * s))) + (l * s)) + (- w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((((1 - l) * ((1 / 2) * w)) + ((1 - l) * ((1 / 2) * s))) + (l * s)) - w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K419(((((1 - l) * ((1 / 2) * w)) + ((1 - l) * ((1 / 2) * s))) + (l * s)),K448(w)) is V16() V21() set
((1 - l) * ((1 / 2) * s)) + (l * s) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 - l) * ((1 / 2) * s)),(l * s)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - l) * ((1 / 2) * s)) + (l * s) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - l) * ((1 / 2) * w)) + (((1 - l) * ((1 / 2) * s)) + (l * s)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 - l) * ((1 / 2) * w)),(((1 - l) * ((1 / 2) * s)) + (l * s))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - l) * ((1 / 2) * w)) + (((1 - l) * ((1 / 2) * s)) + (l * s)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((1 - l) * ((1 / 2) * w)) + (((1 - l) * ((1 / 2) * s)) + (l * s))) - w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K382((TOP-REAL a),(((1 - l) * ((1 / 2) * w)) + (((1 - l) * ((1 / 2) * s)) + (l * s))),(- w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(((1 - l) * ((1 / 2) * w)) + (((1 - l) * ((1 / 2) * s)) + (l * s))),(- w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(((1 - l) * ((1 / 2) * w)) + (((1 - l) * ((1 / 2) * s)) + (l * s))) + (- w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((1 - l) * ((1 / 2) * w)) + (((1 - l) * ((1 / 2) * s)) + (l * s))) - w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K419((((1 - l) * ((1 / 2) * w)) + (((1 - l) * ((1 / 2) * s)) + (l * s))),K448(w)) is V16() V21() set
((1 - l) * ((1 / 2) * w)) - w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K382((TOP-REAL a),((1 - l) * ((1 / 2) * w)),(- w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 - l) * ((1 / 2) * w)),(- w)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - l) * ((1 / 2) * w)) + (- w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - l) * ((1 / 2) * w)) - w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K419(((1 - l) * ((1 / 2) * w)),K448(w)) is V16() V21() set
(((1 - l) * ((1 / 2) * w)) - w) + (((1 - l) * ((1 / 2) * s)) + (l * s)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(((1 - l) * ((1 / 2) * w)) - w),(((1 - l) * ((1 / 2) * s)) + (l * s))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(((1 - l) * ((1 / 2) * w)) - w) + (((1 - l) * ((1 / 2) * s)) + (l * s)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
1 * w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
1 * w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - l) * ((1 / 2) * w)) - (1 * w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- (1 * w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- (1 * w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(- 1) * (1 * w) is V16() V21() set
K382((TOP-REAL a),((1 - l) * ((1 / 2) * w)),(- (1 * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 - l) * ((1 / 2) * w)),(- (1 * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - l) * ((1 / 2) * w)) + (- (1 * w)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - l) * ((1 / 2) * w)) - (1 * w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K448((1 * w)) is V16() V21() complex-yielding set
K419(((1 - l) * ((1 / 2) * w)),K448((1 * w))) is V16() V21() set
(((1 - l) * ((1 / 2) * w)) - (1 * w)) + (((1 - l) * ((1 / 2) * s)) + (l * s)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(((1 - l) * ((1 / 2) * w)) - (1 * w)),(((1 - l) * ((1 / 2) * s)) + (l * s))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(((1 - l) * ((1 / 2) * w)) - (1 * w)) + (((1 - l) * ((1 / 2) * s)) + (l * s)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(1 - l) * (1 / 2) is V11() real ext-real Element of REAL
((1 - l) * (1 / 2)) * w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - l) * (1 / 2)) * w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((1 - l) * (1 / 2)) * w) - (1 * w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K382((TOP-REAL a),(((1 - l) * (1 / 2)) * w),(- (1 * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(((1 - l) * (1 / 2)) * w),(- (1 * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(((1 - l) * (1 / 2)) * w) + (- (1 * w)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((1 - l) * (1 / 2)) * w) - (1 * w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K419((((1 - l) * (1 / 2)) * w),K448((1 * w))) is V16() V21() set
((((1 - l) * (1 / 2)) * w) - (1 * w)) + (((1 - l) * ((1 / 2) * s)) + (l * s)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((((1 - l) * (1 / 2)) * w) - (1 * w)),(((1 - l) * ((1 / 2) * s)) + (l * s))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((((1 - l) * (1 / 2)) * w) - (1 * w)) + (((1 - l) * ((1 / 2) * s)) + (l * s)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - l) * (1 / 2)) - 1 is V11() real ext-real Element of REAL
((1 - l) * (1 / 2)) + (- 1) is V11() real ext-real set
(((1 - l) * (1 / 2)) - 1) * w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(((1 - l) * (1 / 2)) - 1) * w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((((1 - l) * (1 / 2)) - 1) * w) + (((1 - l) * ((1 / 2) * s)) + (l * s)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((((1 - l) * (1 / 2)) - 1) * w),(((1 - l) * ((1 / 2) * s)) + (l * s))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((((1 - l) * (1 / 2)) - 1) * w) + (((1 - l) * ((1 / 2) * s)) + (l * s)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
- (1 / 2) is V11() real ext-real non positive Element of REAL
l * (1 / 2) is V11() real ext-real Element of REAL
(- (1 / 2)) - (l * (1 / 2)) is V11() real ext-real Element of REAL
- (l * (1 / 2)) is V11() real ext-real set
(- (1 / 2)) + (- (l * (1 / 2))) is V11() real ext-real set
((- (1 / 2)) - (l * (1 / 2))) * w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((- (1 / 2)) - (l * (1 / 2))) * w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - l) * (1 / 2)) * s is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - l) * (1 / 2)) * s is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((1 - l) * (1 / 2)) * s) + (l * s) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(((1 - l) * (1 / 2)) * s),(l * s)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(((1 - l) * (1 / 2)) * s) + (l * s) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((- (1 / 2)) - (l * (1 / 2))) * w) + ((((1 - l) * (1 / 2)) * s) + (l * s)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(((- (1 / 2)) - (l * (1 / 2))) * w),((((1 - l) * (1 / 2)) * s) + (l * s))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(((- (1 / 2)) - (l * (1 / 2))) * w) + ((((1 - l) * (1 / 2)) * s) + (l * s)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - l) * (1 / 2)) + l is V11() real ext-real Element of REAL
(((1 - l) * (1 / 2)) + l) * s is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(((1 - l) * (1 / 2)) + l) * s is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((- (1 / 2)) - (l * (1 / 2))) * w) + ((((1 - l) * (1 / 2)) + l) * s) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(((- (1 / 2)) - (l * (1 / 2))) * w),((((1 - l) * (1 / 2)) + l) * s)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(((- (1 / 2)) - (l * (1 / 2))) * w) + ((((1 - l) * (1 / 2)) + l) * s) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(1 / 2) + (l * (1 / 2)) is V11() real ext-real Element of REAL
- ((1 / 2) + (l * (1 / 2))) is V11() real ext-real Element of REAL
(- ((1 / 2) + (l * (1 / 2)))) * w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(- ((1 / 2) + (l * (1 / 2)))) * w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 / 2) + (l * (1 / 2))) * s is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 / 2) + (l * (1 / 2))) * s is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((- ((1 / 2) + (l * (1 / 2)))) * w) + (((1 / 2) + (l * (1 / 2))) * s) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((- ((1 / 2) + (l * (1 / 2)))) * w),(((1 / 2) + (l * (1 / 2))) * s)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((- ((1 / 2) + (l * (1 / 2)))) * w) + (((1 / 2) + (l * (1 / 2))) * s) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 / 2) + (l * (1 / 2))) * w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 / 2) + (l * (1 / 2))) * w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((1 / 2) + (l * (1 / 2))) * s) - (((1 / 2) + (l * (1 / 2))) * w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- (((1 / 2) + (l * (1 / 2))) * w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- (((1 / 2) + (l * (1 / 2))) * w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(- 1) * (((1 / 2) + (l * (1 / 2))) * w) is V16() V21() set
K382((TOP-REAL a),(((1 / 2) + (l * (1 / 2))) * s),(- (((1 / 2) + (l * (1 / 2))) * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(((1 / 2) + (l * (1 / 2))) * s),(- (((1 / 2) + (l * (1 / 2))) * w))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(((1 / 2) + (l * (1 / 2))) * s) + (- (((1 / 2) + (l * (1 / 2))) * w)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((1 / 2) + (l * (1 / 2))) * s) - (((1 / 2) + (l * (1 / 2))) * w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K448((((1 / 2) + (l * (1 / 2))) * w)) is V16() V21() complex-yielding set
K419((((1 / 2) + (l * (1 / 2))) * s),K448((((1 / 2) + (l * (1 / 2))) * w))) is V16() V21() set
((1 / 2) + (l * (1 / 2))) * (s - w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 / 2) + (l * (1 / 2))) * (s - w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
1 + l is V11() real ext-real Element of REAL
(1 + l) / 2 is V11() real ext-real Element of REAL
(1 + l) * (2 ") is V11() real ext-real set
M is set
(((1 - l) * (1 / 2)) * w) + ((1 - l) * ((1 / 2) * s)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(((1 - l) * (1 / 2)) * w),((1 - l) * ((1 / 2) * s))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(((1 - l) * (1 / 2)) * w) + ((1 - l) * ((1 / 2) * s)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((((1 - l) * (1 / 2)) * w) + ((1 - l) * ((1 / 2) * s))) + (l * s) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((((1 - l) * (1 / 2)) * w) + ((1 - l) * ((1 / 2) * s))),(l * s)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((((1 - l) * (1 / 2)) * w) + ((1 - l) * ((1 / 2) * s))) + (l * s) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((1 - l) * (1 / 2)) * w) + (((1 - l) * (1 / 2)) * s) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(((1 - l) * (1 / 2)) * w),(((1 - l) * (1 / 2)) * s)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(((1 - l) * (1 / 2)) * w) + (((1 - l) * (1 / 2)) * s) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((((1 - l) * (1 / 2)) * w) + (((1 - l) * (1 / 2)) * s)) + (l * s) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((((1 - l) * (1 / 2)) * w) + (((1 - l) * (1 / 2)) * s)),(l * s)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((((1 - l) * (1 / 2)) * w) + (((1 - l) * (1 / 2)) * s)) + (l * s) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((1 - l) * (1 / 2)) * w) + ((((1 - l) * (1 / 2)) * s) + (l * s)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(((1 - l) * (1 / 2)) * w),((((1 - l) * (1 / 2)) * s) + (l * s))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(((1 - l) * (1 / 2)) * w) + ((((1 - l) * (1 / 2)) * s) + (l * s)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((1 - l) * (1 / 2)) * w) + ((((1 - l) * (1 / 2)) + l) * s) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(((1 - l) * (1 / 2)) * w),((((1 - l) * (1 / 2)) + l) * s)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(((1 - l) * (1 / 2)) * w) + ((((1 - l) * (1 / 2)) + l) * s) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
1 - ((1 + l) / 2) is V11() real ext-real Element of REAL
- ((1 + l) / 2) is V11() real ext-real set
1 + (- ((1 + l) / 2)) is V11() real ext-real set
(1 - ((1 + l) / 2)) * w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(1 - ((1 + l) / 2)) * w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 + l) / 2) * s is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 + l) / 2) * s is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - ((1 + l) / 2)) * w) + (((1 + l) / 2) * s) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 - ((1 + l) / 2)) * w),(((1 + l) / 2) * s)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - ((1 + l) / 2)) * w) + (((1 + l) / 2) * s) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
m is set
M is V11() real ext-real set
1 - M is V11() real ext-real Element of REAL
- M is V11() real ext-real set
1 + (- M) is V11() real ext-real set
(1 - M) * w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(1 - M) * w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
M * s is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
M * s is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - M) * w) + (M * s) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 - M) * w),(M * s)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - M) * w) + (M * s) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
2 * M is V11() real ext-real Element of REAL
(2 * M) - 1 is V11() real ext-real Element of REAL
(2 * M) + (- 1) is V11() real ext-real set
2 * 1 is ordinal natural V11() real ext-real non negative Element of REAL
(2 * 1) - 1 is V11() real ext-real Element of REAL
(2 * 1) + (- 1) is V11() real ext-real set
1 - ((2 * M) - 1) is V11() real ext-real Element of REAL
- ((2 * M) - 1) is V11() real ext-real set
1 + (- ((2 * M) - 1)) is V11() real ext-real set
(1 - ((2 * M) - 1)) * (((1 / 2) * w) + ((1 / 2) * s)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(1 - ((2 * M) - 1)) * (((1 / 2) * w) + ((1 / 2) * s)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((2 * M) - 1) * s is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((2 * M) - 1) * s is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - ((2 * M) - 1)) * (((1 / 2) * w) + ((1 / 2) * s))) + (((2 * M) - 1) * s) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 - ((2 * M) - 1)) * (((1 / 2) * w) + ((1 / 2) * s))),(((2 * M) - 1) * s)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - ((2 * M) - 1)) * (((1 / 2) * w) + ((1 / 2) * s))) + (((2 * M) - 1) * s) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(1 - ((2 * M) - 1)) * ((1 / 2) * w) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(1 - ((2 * M) - 1)) * ((1 / 2) * w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(1 - ((2 * M) - 1)) * ((1 / 2) * s) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(1 - ((2 * M) - 1)) * ((1 / 2) * s) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - ((2 * M) - 1)) * ((1 / 2) * w)) + ((1 - ((2 * M) - 1)) * ((1 / 2) * s)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 - ((2 * M) - 1)) * ((1 / 2) * w)),((1 - ((2 * M) - 1)) * ((1 / 2) * s))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - ((2 * M) - 1)) * ((1 / 2) * w)) + ((1 - ((2 * M) - 1)) * ((1 / 2) * s)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((1 - ((2 * M) - 1)) * ((1 / 2) * w)) + ((1 - ((2 * M) - 1)) * ((1 / 2) * s))) + (((2 * M) - 1) * s) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(((1 - ((2 * M) - 1)) * ((1 / 2) * w)) + ((1 - ((2 * M) - 1)) * ((1 / 2) * s))),(((2 * M) - 1) * s)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(((1 - ((2 * M) - 1)) * ((1 / 2) * w)) + ((1 - ((2 * M) - 1)) * ((1 / 2) * s))) + (((2 * M) - 1) * s) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(1 - ((2 * M) - 1)) * (1 / 2) is V11() real ext-real Element of REAL
((1 - ((2 * M) - 1)) * (1 / 2)) * w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - ((2 * M) - 1)) * (1 / 2)) * w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((1 - ((2 * M) - 1)) * (1 / 2)) * w) + ((1 - ((2 * M) - 1)) * ((1 / 2) * s)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(((1 - ((2 * M) - 1)) * (1 / 2)) * w),((1 - ((2 * M) - 1)) * ((1 / 2) * s))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(((1 - ((2 * M) - 1)) * (1 / 2)) * w) + ((1 - ((2 * M) - 1)) * ((1 / 2) * s)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((((1 - ((2 * M) - 1)) * (1 / 2)) * w) + ((1 - ((2 * M) - 1)) * ((1 / 2) * s))) + (((2 * M) - 1) * s) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((((1 - ((2 * M) - 1)) * (1 / 2)) * w) + ((1 - ((2 * M) - 1)) * ((1 / 2) * s))),(((2 * M) - 1) * s)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((((1 - ((2 * M) - 1)) * (1 / 2)) * w) + ((1 - ((2 * M) - 1)) * ((1 / 2) * s))) + (((2 * M) - 1) * s) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - ((2 * M) - 1)) * (1 / 2)) * s is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - ((2 * M) - 1)) * (1 / 2)) * s is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((1 - ((2 * M) - 1)) * (1 / 2)) * w) + (((1 - ((2 * M) - 1)) * (1 / 2)) * s) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(((1 - ((2 * M) - 1)) * (1 / 2)) * w),(((1 - ((2 * M) - 1)) * (1 / 2)) * s)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(((1 - ((2 * M) - 1)) * (1 / 2)) * w) + (((1 - ((2 * M) - 1)) * (1 / 2)) * s) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((((1 - ((2 * M) - 1)) * (1 / 2)) * w) + (((1 - ((2 * M) - 1)) * (1 / 2)) * s)) + (((2 * M) - 1) * s) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((((1 - ((2 * M) - 1)) * (1 / 2)) * w) + (((1 - ((2 * M) - 1)) * (1 / 2)) * s)),(((2 * M) - 1) * s)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((((1 - ((2 * M) - 1)) * (1 / 2)) * w) + (((1 - ((2 * M) - 1)) * (1 / 2)) * s)) + (((2 * M) - 1) * s) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((1 - ((2 * M) - 1)) * (1 / 2)) * s) + (((2 * M) - 1) * s) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(((1 - ((2 * M) - 1)) * (1 / 2)) * s),(((2 * M) - 1) * s)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(((1 - ((2 * M) - 1)) * (1 / 2)) * s) + (((2 * M) - 1) * s) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((1 - ((2 * M) - 1)) * (1 / 2)) * w) + ((((1 - ((2 * M) - 1)) * (1 / 2)) * s) + (((2 * M) - 1) * s)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(((1 - ((2 * M) - 1)) * (1 / 2)) * w),((((1 - ((2 * M) - 1)) * (1 / 2)) * s) + (((2 * M) - 1) * s))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(((1 - ((2 * M) - 1)) * (1 / 2)) * w) + ((((1 - ((2 * M) - 1)) * (1 / 2)) * s) + (((2 * M) - 1) * s)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - ((2 * M) - 1)) * (1 / 2)) + ((2 * M) - 1) is V11() real ext-real Element of REAL
(((1 - ((2 * M) - 1)) * (1 / 2)) + ((2 * M) - 1)) * s is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(((1 - ((2 * M) - 1)) * (1 / 2)) + ((2 * M) - 1)) * s is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((1 - ((2 * M) - 1)) * (1 / 2)) * w) + ((((1 - ((2 * M) - 1)) * (1 / 2)) + ((2 * M) - 1)) * s) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(((1 - ((2 * M) - 1)) * (1 / 2)) * w),((((1 - ((2 * M) - 1)) * (1 / 2)) + ((2 * M) - 1)) * s)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(((1 - ((2 * M) - 1)) * (1 / 2)) * w) + ((((1 - ((2 * M) - 1)) * (1 / 2)) + ((2 * M) - 1)) * s) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
s - t is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K382((TOP-REAL a),s,(- t)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),s,(- t)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
s + (- t) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
s - t is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K419(s,K448(t)) is V16() V21() set
|.(s - t).| is V11() real ext-real non negative Element of REAL
sqr (s - t) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt ((s - t),(s - t)) is V16() V21() set
Sum (sqr (s - t)) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (s - t))) is V11() real ext-real Element of REAL
LSeg (w,s) is Element of K6( the carrier of (TOP-REAL a))
{ (((1 - b1) * w) + (b1 * s)) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
(LSeg (w,s)) /\ (a,t,b) is Element of K6( the carrier of (TOP-REAL a))
{w} is non empty V24() set
a is ordinal natural V11() real ext-real non negative set
TOP-REAL a is non empty TopSpace-like V126() V191() V192() V209() V210() V211() V212() V213() V214() V215() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL a) is non empty set
b is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
r is non empty V11() real ext-real non positive negative set
(a,b,r) is closed Element of K6( the carrier of (TOP-REAL a))
K6( the carrier of (TOP-REAL a)) is set
{ b1 where b1 is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a) : |.(b1 - b).| = r } is set
w is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
w - b is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- b is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- b is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
- 1 is V11() real ext-real non positive set
(- 1) * b is V16() V21() set
K382((TOP-REAL a),w,(- b)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
the U7 of (TOP-REAL a) is V16() V21() V30(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) Element of K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)))
K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)) is V16() set
K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) is V16() set
K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a))) is set
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),w,(- b)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
w + (- b) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
w - b is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K448(b) is V16() V21() complex-yielding set
K419(w,K448(b)) is V16() V21() set
|.(w - b).| is V11() real ext-real non negative Element of REAL
sqr (w - b) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt ((w - b),(w - b)) is V16() V21() set
Sum (sqr (w - b)) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (w - b))) is V11() real ext-real Element of REAL
a is non empty ordinal natural V11() real ext-real positive non negative set
TOP-REAL a is non empty TopSpace-like V126() V191() V192() V209() V210() V211() V212() V213() V214() V215() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL a) is non empty set
b is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
r is V11() real ext-real non negative set
(a,b,r) is closed Element of K6( the carrier of (TOP-REAL a))
K6( the carrier of (TOP-REAL a)) is set
{ b1 where b1 is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a) : |.(b1 - b).| = r } is set
Euclid a is non empty strict Reflexive discerning V103() triangle MetrStruct
REAL a is non empty V24() FinSequence-membered FinSequenceSet of REAL
a -tuples_on REAL is V24() FinSequence-membered FinSequenceSet of REAL
Pitag_dist a is V16() V21() V30(K7((REAL a),(REAL a)), REAL ) complex-yielding ext-real-valued real-valued Element of K6(K7(K7((REAL a),(REAL a)),REAL))
K7((REAL a),(REAL a)) is V16() set
K7(K7((REAL a),(REAL a)),REAL) is V16() complex-yielding ext-real-valued real-valued set
K6(K7(K7((REAL a),(REAL a)),REAL)) is set
MetrStruct(# (REAL a),(Pitag_dist a) #) is strict MetrStruct
the carrier of (Euclid a) is non empty set
w is Element of the carrier of (Euclid a)
Sphere (w,r) is Element of K6( the carrier of (Euclid a))
K6( the carrier of (Euclid a)) is set
{w} is non empty set
s is non empty V11() real ext-real positive non negative set
(a,b,s) is non empty open convex Element of K6( the carrier of (TOP-REAL a))
{ b1 where b1 is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a) : not s <= |.(b1 - b).| } is set
t is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
1.REAL a is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
1* a is V16() V19( NAT ) V20( REAL ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL a
a |-> 1 is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of a -tuples_on REAL
t + (1.REAL a) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
the U7 of (TOP-REAL a) is V16() V21() V30(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) Element of K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)))
K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)) is V16() set
K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a)) is V16() set
K6(K7(K7( the carrier of (TOP-REAL a), the carrier of (TOP-REAL a)), the carrier of (TOP-REAL a))) is set
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),t,(1.REAL a)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
t + (1.REAL a) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(t + (1.REAL a)) - t is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- t is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- t is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
- 1 is V11() real ext-real non positive set
(- 1) * t is V16() V21() set
K382((TOP-REAL a),(t + (1.REAL a)),(- t)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),(t + (1.REAL a)),(- t)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(t + (1.REAL a)) + (- t) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(t + (1.REAL a)) - t is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K448(t) is V16() V21() complex-yielding set
K419((t + (1.REAL a)),K448(t)) is V16() V21() set
t - b is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- b is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
- b is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(- 1) * b is V16() V21() set
K382((TOP-REAL a),t,(- b)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),t,(- b)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
t + (- b) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
t - b is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K448(b) is V16() V21() complex-yielding set
K419(t,K448(b)) is V16() V21() set
|(((t + (1.REAL a)) - t),(t - b))| is V11() real ext-real Element of REAL
2 * |(((t + (1.REAL a)) - t),(t - b))| is V11() real ext-real Element of REAL
- (2 * |(((t + (1.REAL a)) - t),(t - b))|) is V11() real ext-real Element of REAL
S is V16() V19( NAT ) V20( REAL ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL a
G is V16() V19( NAT ) V20( REAL ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL a
S - G is V16() V19( NAT ) V20( REAL ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL a
K448(G) is V16() V21() complex-yielding set
(- 1) * G is V16() V21() set
K419(S,K448(G)) is V16() V21() set
sqr (S - G) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of a -tuples_on REAL
mlt ((S - G),(S - G)) is V16() V21() set
Sum (sqr (S - G)) is V11() real ext-real Element of REAL
T is V16() V19( NAT ) V20( REAL ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL a
G - T is V16() V19( NAT ) V20( REAL ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL a
K448(T) is V16() V21() complex-yielding set
(- 1) * T is V16() V21() set
K419(G,K448(T)) is V16() V21() set
sqr (G - T) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of a -tuples_on REAL
mlt ((G - T),(G - T)) is V16() V21() set
Sum (sqr (G - T)) is V11() real ext-real Element of REAL
s ^2 is V11() real ext-real set
s * s is V11() real ext-real non negative set
(Sum (sqr (G - T))) - (s ^2) is V11() real ext-real Element of REAL
- (s ^2) is V11() real ext-real set
(Sum (sqr (G - T))) + (- (s ^2)) is V11() real ext-real set
delta ((Sum (sqr (S - G))),(2 * |(((t + (1.REAL a)) - t),(t - b))|),((Sum (sqr (G - T))) - (s ^2))) is V11() real ext-real Element of REAL
sqrt (delta ((Sum (sqr (S - G))),(2 * |(((t + (1.REAL a)) - t),(t - b))|),((Sum (sqr (G - T))) - (s ^2)))) is V11() real ext-real Element of REAL
(- (2 * |(((t + (1.REAL a)) - t),(t - b))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |(((t + (1.REAL a)) - t),(t - b))|),((Sum (sqr (G - T))) - (s ^2))))) is V11() real ext-real Element of REAL
2 * (Sum (sqr (S - G))) is V11() real ext-real Element of REAL
((- (2 * |(((t + (1.REAL a)) - t),(t - b))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |(((t + (1.REAL a)) - t),(t - b))|),((Sum (sqr (G - T))) - (s ^2)))))) / (2 * (Sum (sqr (S - G)))) is V11() real ext-real Element of REAL
(2 * (Sum (sqr (S - G)))) " is V11() real ext-real set
((- (2 * |(((t + (1.REAL a)) - t),(t - b))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |(((t + (1.REAL a)) - t),(t - b))|),((Sum (sqr (G - T))) - (s ^2)))))) * ((2 * (Sum (sqr (S - G)))) ") is V11() real ext-real set
(a,t,(t + (1.REAL a))) is Element of K6( the carrier of (TOP-REAL a))
{ (((1 - b1) * t) + (b1 * (t + (1.REAL a)))) where b1 is V11() real ext-real Element of REAL : 0 <= b1 } is set
(a,b,s) is closed Element of K6( the carrier of (TOP-REAL a))
{ b1 where b1 is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a) : |.(b1 - b).| = s } is set
(a,t,(t + (1.REAL a))) /\ (a,b,s) is Element of K6( the carrier of (TOP-REAL a))
1 - (((- (2 * |(((t + (1.REAL a)) - t),(t - b))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |(((t + (1.REAL a)) - t),(t - b))|),((Sum (sqr (G - T))) - (s ^2)))))) / (2 * (Sum (sqr (S - G))))) is V11() real ext-real Element of REAL
- (((- (2 * |(((t + (1.REAL a)) - t),(t - b))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |(((t + (1.REAL a)) - t),(t - b))|),((Sum (sqr (G - T))) - (s ^2)))))) / (2 * (Sum (sqr (S - G))))) is V11() real ext-real set
1 + (- (((- (2 * |(((t + (1.REAL a)) - t),(t - b))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |(((t + (1.REAL a)) - t),(t - b))|),((Sum (sqr (G - T))) - (s ^2)))))) / (2 * (Sum (sqr (S - G)))))) is V11() real ext-real set
(1 - (((- (2 * |(((t + (1.REAL a)) - t),(t - b))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |(((t + (1.REAL a)) - t),(t - b))|),((Sum (sqr (G - T))) - (s ^2)))))) / (2 * (Sum (sqr (S - G)))))) * t is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(1 - (((- (2 * |(((t + (1.REAL a)) - t),(t - b))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |(((t + (1.REAL a)) - t),(t - b))|),((Sum (sqr (G - T))) - (s ^2)))))) / (2 * (Sum (sqr (S - G)))))) * t is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((- (2 * |(((t + (1.REAL a)) - t),(t - b))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |(((t + (1.REAL a)) - t),(t - b))|),((Sum (sqr (G - T))) - (s ^2)))))) / (2 * (Sum (sqr (S - G))))) * (t + (1.REAL a)) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
(((- (2 * |(((t + (1.REAL a)) - t),(t - b))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |(((t + (1.REAL a)) - t),(t - b))|),((Sum (sqr (G - T))) - (s ^2)))))) / (2 * (Sum (sqr (S - G))))) * (t + (1.REAL a)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - (((- (2 * |(((t + (1.REAL a)) - t),(t - b))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |(((t + (1.REAL a)) - t),(t - b))|),((Sum (sqr (G - T))) - (s ^2)))))) / (2 * (Sum (sqr (S - G)))))) * t) + ((((- (2 * |(((t + (1.REAL a)) - t),(t - b))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |(((t + (1.REAL a)) - t),(t - b))|),((Sum (sqr (G - T))) - (s ^2)))))) / (2 * (Sum (sqr (S - G))))) * (t + (1.REAL a))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
K350( the carrier of (TOP-REAL a), the U7 of (TOP-REAL a),((1 - (((- (2 * |(((t + (1.REAL a)) - t),(t - b))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |(((t + (1.REAL a)) - t),(t - b))|),((Sum (sqr (G - T))) - (s ^2)))))) / (2 * (Sum (sqr (S - G)))))) * t),((((- (2 * |(((t + (1.REAL a)) - t),(t - b))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |(((t + (1.REAL a)) - t),(t - b))|),((Sum (sqr (G - T))) - (s ^2)))))) / (2 * (Sum (sqr (S - G))))) * (t + (1.REAL a)))) is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
((1 - (((- (2 * |(((t + (1.REAL a)) - t),(t - b))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |(((t + (1.REAL a)) - t),(t - b))|),((Sum (sqr (G - T))) - (s ^2)))))) / (2 * (Sum (sqr (S - G)))))) * t) + ((((- (2 * |(((t + (1.REAL a)) - t),(t - b))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |(((t + (1.REAL a)) - t),(t - b))|),((Sum (sqr (G - T))) - (s ^2)))))) / (2 * (Sum (sqr (S - G))))) * (t + (1.REAL a))) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
s is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
{s} is non empty V24() set
a is ordinal natural V11() real ext-real non negative V33() V34() V179() V180() V181() V182() V183() V184() Element of NAT
TOP-REAL a is non empty TopSpace-like V126() V191() V192() V209() V210() V211() V212() V213() V214() V215() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL a) is non empty set
r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
b is V11() real ext-real set
(a,r,b) is closed bounded Element of K6( the carrier of (TOP-REAL a))
K6( the carrier of (TOP-REAL a)) is set
{ b1 where b1 is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a) : |.(b1 - r).| = b } is set
a is ordinal natural V11() real ext-real non negative V33() V34() V179() V180() V181() V182() V183() V184() Element of NAT
TOP-REAL a is non empty TopSpace-like V126() V191() V192() V209() V210() V211() V212() V213() V214() V215() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL a) is non empty set
r is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a)
b is V11() real ext-real set
(a,r,b) is closed bounded Element of K6( the carrier of (TOP-REAL a))
K6( the carrier of (TOP-REAL a)) is set
{ b1 where b1 is V16() V19( NAT ) V21() V37() V44(a) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL a) : |.(b1 - r).| = b } is set
a is V11() real ext-real set
b is V11() real ext-real set
r is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
a * r is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
a * r is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
r `1 is V11() real ext-real Element of REAL
a * (r `1) is V11() real ext-real Element of REAL
w is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
b * w is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
b * w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(a * r) + (b * w) is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) is V16() V21() V30(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2)) Element of K6(K7(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2)))
K7(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2)) is V16() set
K6(K7(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2))) is set
K350( the carrier of (TOP-REAL 2), the U7 of (TOP-REAL 2),(a * r),(b * w)) is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(a * r) + (b * w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((a * r) + (b * w)) `1 is V11() real ext-real Element of REAL
w `1 is V11() real ext-real Element of REAL
b * (w `1) is V11() real ext-real Element of REAL
(a * (r `1)) + (b * (w `1)) is V11() real ext-real Element of REAL
(a * r) `1 is V11() real ext-real Element of REAL
(b * w) `1 is V11() real ext-real Element of REAL
((a * r) `1) + ((b * w) `1) is V11() real ext-real Element of REAL
(a * (r `1)) + ((b * w) `1) is V11() real ext-real Element of REAL
a is V11() real ext-real set
b is V11() real ext-real set
r is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
a * r is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
a * r is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
r `2 is V11() real ext-real Element of REAL
a * (r `2) is V11() real ext-real Element of REAL
w is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
b * w is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
b * w is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(a * r) + (b * w) is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) is V16() V21() V30(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2)) Element of K6(K7(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2)))
K7(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2)) is V16() set
K6(K7(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2))) is set
K350( the carrier of (TOP-REAL 2), the U7 of (TOP-REAL 2),(a * r),(b * w)) is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(a * r) + (b * w) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((a * r) + (b * w)) `2 is V11() real ext-real Element of REAL
w `2 is V11() real ext-real Element of REAL
b * (w `2) is V11() real ext-real Element of REAL
(a * (r `2)) + (b * (w `2)) is V11() real ext-real Element of REAL
(a * r) `2 is V11() real ext-real Element of REAL
(b * w) `2 is V11() real ext-real Element of REAL
((a * r) `2) + ((b * w) `2) is V11() real ext-real Element of REAL
(a * (r `2)) + ((b * w) `2) is V11() real ext-real Element of REAL
a is V11() real ext-real set
b is V11() real ext-real set
|[a,b]| is non empty V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
r is V11() real ext-real set
circle (a,b,r) is Element of K6( the carrier of (TOP-REAL 2))
w is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
w - |[a,b]| is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- |[a,b]| is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- |[a,b]| is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
- 1 is V11() real ext-real non positive set
(- 1) * |[a,b]| is V16() V21() set
K382((TOP-REAL 2),w,(- |[a,b]|)) is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) is V16() V21() V30(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2)) Element of K6(K7(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2)))
K7(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2)) is V16() set
K6(K7(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2))) is set
K350( the carrier of (TOP-REAL 2), the U7 of (TOP-REAL 2),w,(- |[a,b]|)) is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
w + (- |[a,b]|) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
w - |[a,b]| is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K448(|[a,b]|) is V16() V21() complex-yielding set
K419(w,K448(|[a,b]|)) is V16() V21() set
|.(w - |[a,b]|).| is V11() real ext-real non negative Element of REAL
sqr (w - |[a,b]|) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt ((w - |[a,b]|),(w - |[a,b]|)) is V16() V21() set
Sum (sqr (w - |[a,b]|)) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (w - |[a,b]|))) is V11() real ext-real Element of REAL
{ b1 where b1 is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2) : |.(b1 - |[a,b]|).| = r } is set
s is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
s - |[a,b]| is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K382((TOP-REAL 2),s,(- |[a,b]|)) is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K350( the carrier of (TOP-REAL 2), the U7 of (TOP-REAL 2),s,(- |[a,b]|)) is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
s + (- |[a,b]|) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
s - |[a,b]| is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K419(s,K448(|[a,b]|)) is V16() V21() set
|.(s - |[a,b]|).| is V11() real ext-real non negative Element of REAL
sqr (s - |[a,b]|) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt ((s - |[a,b]|),(s - |[a,b]|)) is V16() V21() set
Sum (sqr (s - |[a,b]|)) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (s - |[a,b]|))) is V11() real ext-real Element of REAL
a is V11() real ext-real set
b is V11() real ext-real set
|[a,b]| is non empty V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
r is V11() real ext-real set
closed_inside_of_circle (a,b,r) is Element of K6( the carrier of (TOP-REAL 2))
w is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
w - |[a,b]| is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- |[a,b]| is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- |[a,b]| is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
- 1 is V11() real ext-real non positive set
(- 1) * |[a,b]| is V16() V21() set
K382((TOP-REAL 2),w,(- |[a,b]|)) is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) is V16() V21() V30(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2)) Element of K6(K7(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2)))
K7(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2)) is V16() set
K6(K7(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2))) is set
K350( the carrier of (TOP-REAL 2), the U7 of (TOP-REAL 2),w,(- |[a,b]|)) is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
w + (- |[a,b]|) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
w - |[a,b]| is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K448(|[a,b]|) is V16() V21() complex-yielding set
K419(w,K448(|[a,b]|)) is V16() V21() set
|.(w - |[a,b]|).| is V11() real ext-real non negative Element of REAL
sqr (w - |[a,b]|) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt ((w - |[a,b]|),(w - |[a,b]|)) is V16() V21() set
Sum (sqr (w - |[a,b]|)) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (w - |[a,b]|))) is V11() real ext-real Element of REAL
{ b1 where b1 is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2) : |.(b1 - |[a,b]|).| <= r } is set
s is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
s - |[a,b]| is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K382((TOP-REAL 2),s,(- |[a,b]|)) is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K350( the carrier of (TOP-REAL 2), the U7 of (TOP-REAL 2),s,(- |[a,b]|)) is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
s + (- |[a,b]|) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
s - |[a,b]| is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K419(s,K448(|[a,b]|)) is V16() V21() set
|.(s - |[a,b]|).| is V11() real ext-real non negative Element of REAL
sqr (s - |[a,b]|) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt ((s - |[a,b]|),(s - |[a,b]|)) is V16() V21() set
Sum (sqr (s - |[a,b]|)) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (s - |[a,b]|))) is V11() real ext-real Element of REAL
a is V11() real ext-real set
b is V11() real ext-real set
|[a,b]| is non empty V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
r is V11() real ext-real set
inside_of_circle (a,b,r) is Element of K6( the carrier of (TOP-REAL 2))
w is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
w - |[a,b]| is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- |[a,b]| is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- |[a,b]| is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
- 1 is V11() real ext-real non positive set
(- 1) * |[a,b]| is V16() V21() set
K382((TOP-REAL 2),w,(- |[a,b]|)) is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) is V16() V21() V30(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2)) Element of K6(K7(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2)))
K7(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2)) is V16() set
K6(K7(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2))) is set
K350( the carrier of (TOP-REAL 2), the U7 of (TOP-REAL 2),w,(- |[a,b]|)) is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
w + (- |[a,b]|) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
w - |[a,b]| is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K448(|[a,b]|) is V16() V21() complex-yielding set
K419(w,K448(|[a,b]|)) is V16() V21() set
|.(w - |[a,b]|).| is V11() real ext-real non negative Element of REAL
sqr (w - |[a,b]|) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt ((w - |[a,b]|),(w - |[a,b]|)) is V16() V21() set
Sum (sqr (w - |[a,b]|)) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (w - |[a,b]|))) is V11() real ext-real Element of REAL
{ b1 where b1 is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2) : not r <= |.(b1 - |[a,b]|).| } is set
s is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
s - |[a,b]| is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K382((TOP-REAL 2),s,(- |[a,b]|)) is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K350( the carrier of (TOP-REAL 2), the U7 of (TOP-REAL 2),s,(- |[a,b]|)) is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
s + (- |[a,b]|) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
s - |[a,b]| is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K419(s,K448(|[a,b]|)) is V16() V21() set
|.(s - |[a,b]|).| is V11() real ext-real non negative Element of REAL
sqr (s - |[a,b]|) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt ((s - |[a,b]|),(s - |[a,b]|)) is V16() V21() set
Sum (sqr (s - |[a,b]|)) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (s - |[a,b]|))) is V11() real ext-real Element of REAL
a is V11() real ext-real set
b is V11() real ext-real set
r is non empty V11() real ext-real positive non negative set
inside_of_circle (a,b,r) is Element of K6( the carrier of (TOP-REAL 2))
|[a,b]| is non empty V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
|[a,b]| - |[a,b]| is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- |[a,b]| is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- |[a,b]| is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
- 1 is V11() real ext-real non positive set
(- 1) * |[a,b]| is V16() V21() set
K382((TOP-REAL 2),|[a,b]|,(- |[a,b]|)) is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) is V16() V21() V30(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2)) Element of K6(K7(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2)))
K7(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2)) is V16() set
K6(K7(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2))) is set
K350( the carrier of (TOP-REAL 2), the U7 of (TOP-REAL 2),|[a,b]|,(- |[a,b]|)) is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
|[a,b]| + (- |[a,b]|) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
|[a,b]| - |[a,b]| is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K448(|[a,b]|) is V16() V21() complex-yielding set
K419(|[a,b]|,K448(|[a,b]|)) is V16() V21() set
|.(|[a,b]| - |[a,b]|).| is V11() real ext-real non negative Element of REAL
sqr (|[a,b]| - |[a,b]|) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt ((|[a,b]| - |[a,b]|),(|[a,b]| - |[a,b]|)) is V16() V21() set
Sum (sqr (|[a,b]| - |[a,b]|)) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (|[a,b]| - |[a,b]|))) is V11() real ext-real Element of REAL
a is V11() real ext-real set
b is V11() real ext-real set
r is V11() real ext-real non negative set
closed_inside_of_circle (a,b,r) is Element of K6( the carrier of (TOP-REAL 2))
|[a,b]| is non empty V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
|[a,b]| - |[a,b]| is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- |[a,b]| is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- |[a,b]| is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
- 1 is V11() real ext-real non positive set
(- 1) * |[a,b]| is V16() V21() set
K382((TOP-REAL 2),|[a,b]|,(- |[a,b]|)) is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) is V16() V21() V30(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2)) Element of K6(K7(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2)))
K7(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2)) is V16() set
K6(K7(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2))) is set
K350( the carrier of (TOP-REAL 2), the U7 of (TOP-REAL 2),|[a,b]|,(- |[a,b]|)) is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
|[a,b]| + (- |[a,b]|) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
|[a,b]| - |[a,b]| is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K448(|[a,b]|) is V16() V21() complex-yielding set
K419(|[a,b]|,K448(|[a,b]|)) is V16() V21() set
|.(|[a,b]| - |[a,b]|).| is V11() real ext-real non negative Element of REAL
sqr (|[a,b]| - |[a,b]|) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt ((|[a,b]| - |[a,b]|),(|[a,b]| - |[a,b]|)) is V16() V21() set
Sum (sqr (|[a,b]| - |[a,b]|)) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (|[a,b]| - |[a,b]|))) is V11() real ext-real Element of REAL
a is V11() real ext-real set
b is V11() real ext-real set
r is V11() real ext-real set
circle (a,b,r) is Element of K6( the carrier of (TOP-REAL 2))
closed_inside_of_circle (a,b,r) is Element of K6( the carrier of (TOP-REAL 2))
w is set
s is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
|[a,b]| is non empty V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
s - |[a,b]| is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- |[a,b]| is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- |[a,b]| is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
- 1 is V11() real ext-real non positive set
(- 1) * |[a,b]| is V16() V21() set
K382((TOP-REAL 2),s,(- |[a,b]|)) is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) is V16() V21() V30(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2)) Element of K6(K7(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2)))
K7(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2)) is V16() set
K6(K7(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2))) is set
K350( the carrier of (TOP-REAL 2), the U7 of (TOP-REAL 2),s,(- |[a,b]|)) is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
s + (- |[a,b]|) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
s - |[a,b]| is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K448(|[a,b]|) is V16() V21() complex-yielding set
K419(s,K448(|[a,b]|)) is V16() V21() set
|.(s - |[a,b]|).| is V11() real ext-real non negative Element of REAL
sqr (s - |[a,b]|) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt ((s - |[a,b]|),(s - |[a,b]|)) is V16() V21() set
Sum (sqr (s - |[a,b]|)) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (s - |[a,b]|))) is V11() real ext-real Element of REAL
Euclid 2 is non empty strict Reflexive discerning V103() triangle MetrStruct
REAL 2 is non empty V24() FinSequence-membered FinSequenceSet of REAL
2 -tuples_on REAL is V24() FinSequence-membered FinSequenceSet of REAL
Pitag_dist 2 is V16() V21() V30(K7((REAL 2),(REAL 2)), REAL ) complex-yielding ext-real-valued real-valued Element of K6(K7(K7((REAL 2),(REAL 2)),REAL))
K7((REAL 2),(REAL 2)) is V16() set
K7(K7((REAL 2),(REAL 2)),REAL) is V16() complex-yielding ext-real-valued real-valued set
K6(K7(K7((REAL 2),(REAL 2)),REAL)) is set
MetrStruct(# (REAL 2),(Pitag_dist 2) #) is strict MetrStruct
the carrier of (Euclid 2) is non empty set
a is V11() real ext-real set
b is V11() real ext-real set
|[a,b]| is non empty V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
r is V11() real ext-real set
closed_inside_of_circle (a,b,r) is Element of K6( the carrier of (TOP-REAL 2))
w is Element of the carrier of (Euclid 2)
cl_Ball (w,r) is Element of K6( the carrier of (Euclid 2))
K6( the carrier of (Euclid 2)) is set
s is set
t is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
G is Element of the carrier of (Euclid 2)
dist (G,w) is V11() real ext-real Element of REAL
t - |[a,b]| is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- |[a,b]| is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- |[a,b]| is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
- 1 is V11() real ext-real non positive set
(- 1) * |[a,b]| is V16() V21() set
K382((TOP-REAL 2),t,(- |[a,b]|)) is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) is V16() V21() V30(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2)) Element of K6(K7(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2)))
K7(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2)) is V16() set
K6(K7(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2))) is set
K350( the carrier of (TOP-REAL 2), the U7 of (TOP-REAL 2),t,(- |[a,b]|)) is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
t + (- |[a,b]|) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
t - |[a,b]| is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K448(|[a,b]|) is V16() V21() complex-yielding set
K419(t,K448(|[a,b]|)) is V16() V21() set
|.(t - |[a,b]|).| is V11() real ext-real non negative Element of REAL
sqr (t - |[a,b]|) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt ((t - |[a,b]|),(t - |[a,b]|)) is V16() V21() set
Sum (sqr (t - |[a,b]|)) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (t - |[a,b]|))) is V11() real ext-real Element of REAL
s is set
t is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
G is Element of the carrier of (Euclid 2)
dist (G,w) is V11() real ext-real Element of REAL
t - |[a,b]| is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K382((TOP-REAL 2),t,(- |[a,b]|)) is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K350( the carrier of (TOP-REAL 2), the U7 of (TOP-REAL 2),t,(- |[a,b]|)) is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
t + (- |[a,b]|) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
t - |[a,b]| is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K419(t,K448(|[a,b]|)) is V16() V21() set
|.(t - |[a,b]|).| is V11() real ext-real non negative Element of REAL
sqr (t - |[a,b]|) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt ((t - |[a,b]|),(t - |[a,b]|)) is V16() V21() set
Sum (sqr (t - |[a,b]|)) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (t - |[a,b]|))) is V11() real ext-real Element of REAL
a is V11() real ext-real set
b is V11() real ext-real set
|[a,b]| is non empty V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
r is V11() real ext-real set
inside_of_circle (a,b,r) is Element of K6( the carrier of (TOP-REAL 2))
w is Element of the carrier of (Euclid 2)
Ball (w,r) is bounded Element of K6( the carrier of (Euclid 2))
K6( the carrier of (Euclid 2)) is set
s is set
t is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
G is Element of the carrier of (Euclid 2)
dist (G,w) is V11() real ext-real Element of REAL
t - |[a,b]| is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- |[a,b]| is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- |[a,b]| is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
- 1 is V11() real ext-real non positive set
(- 1) * |[a,b]| is V16() V21() set
K382((TOP-REAL 2),t,(- |[a,b]|)) is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) is V16() V21() V30(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2)) Element of K6(K7(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2)))
K7(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2)) is V16() set
K6(K7(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2))) is set
K350( the carrier of (TOP-REAL 2), the U7 of (TOP-REAL 2),t,(- |[a,b]|)) is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
t + (- |[a,b]|) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
t - |[a,b]| is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K448(|[a,b]|) is V16() V21() complex-yielding set
K419(t,K448(|[a,b]|)) is V16() V21() set
|.(t - |[a,b]|).| is V11() real ext-real non negative Element of REAL
sqr (t - |[a,b]|) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt ((t - |[a,b]|),(t - |[a,b]|)) is V16() V21() set
Sum (sqr (t - |[a,b]|)) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (t - |[a,b]|))) is V11() real ext-real Element of REAL
s is set
t is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
G is Element of the carrier of (Euclid 2)
dist (G,w) is V11() real ext-real Element of REAL
t - |[a,b]| is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K382((TOP-REAL 2),t,(- |[a,b]|)) is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K350( the carrier of (TOP-REAL 2), the U7 of (TOP-REAL 2),t,(- |[a,b]|)) is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
t + (- |[a,b]|) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
t - |[a,b]| is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K419(t,K448(|[a,b]|)) is V16() V21() set
|.(t - |[a,b]|).| is V11() real ext-real non negative Element of REAL
sqr (t - |[a,b]|) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt ((t - |[a,b]|),(t - |[a,b]|)) is V16() V21() set
Sum (sqr (t - |[a,b]|)) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (t - |[a,b]|))) is V11() real ext-real Element of REAL
a is V11() real ext-real set
b is V11() real ext-real set
|[a,b]| is non empty V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
r is V11() real ext-real set
circle (a,b,r) is Element of K6( the carrier of (TOP-REAL 2))
w is Element of the carrier of (Euclid 2)
Sphere (w,r) is Element of K6( the carrier of (Euclid 2))
K6( the carrier of (Euclid 2)) is set
s is set
t is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
G is Element of the carrier of (Euclid 2)
dist (G,w) is V11() real ext-real Element of REAL
t - |[a,b]| is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- |[a,b]| is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- |[a,b]| is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
- 1 is V11() real ext-real non positive set
(- 1) * |[a,b]| is V16() V21() set
K382((TOP-REAL 2),t,(- |[a,b]|)) is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) is V16() V21() V30(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2)) Element of K6(K7(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2)))
K7(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2)) is V16() set
K6(K7(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2))) is set
K350( the carrier of (TOP-REAL 2), the U7 of (TOP-REAL 2),t,(- |[a,b]|)) is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
t + (- |[a,b]|) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
t - |[a,b]| is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K448(|[a,b]|) is V16() V21() complex-yielding set
K419(t,K448(|[a,b]|)) is V16() V21() set
|.(t - |[a,b]|).| is V11() real ext-real non negative Element of REAL
sqr (t - |[a,b]|) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt ((t - |[a,b]|),(t - |[a,b]|)) is V16() V21() set
Sum (sqr (t - |[a,b]|)) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (t - |[a,b]|))) is V11() real ext-real Element of REAL
s is set
t is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
G is Element of the carrier of (Euclid 2)
dist (G,w) is V11() real ext-real Element of REAL
t - |[a,b]| is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K382((TOP-REAL 2),t,(- |[a,b]|)) is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K350( the carrier of (TOP-REAL 2), the U7 of (TOP-REAL 2),t,(- |[a,b]|)) is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
t + (- |[a,b]|) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
t - |[a,b]| is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K419(t,K448(|[a,b]|)) is V16() V21() set
|.(t - |[a,b]|).| is V11() real ext-real non negative Element of REAL
sqr (t - |[a,b]|) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt ((t - |[a,b]|),(t - |[a,b]|)) is V16() V21() set
Sum (sqr (t - |[a,b]|)) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (t - |[a,b]|))) is V11() real ext-real Element of REAL
a is V11() real ext-real set
b is V11() real ext-real set
|[a,b]| is non empty V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
r is V11() real ext-real set
(2,|[a,b]|,r) is open bounded convex Element of K6( the carrier of (TOP-REAL 2))
{ b1 where b1 is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2) : not r <= |.(b1 - |[a,b]|).| } is set
inside_of_circle (a,b,r) is Element of K6( the carrier of (TOP-REAL 2))
w is Element of the carrier of (Euclid 2)
Ball (w,r) is bounded Element of K6( the carrier of (Euclid 2))
K6( the carrier of (Euclid 2)) is set
a is V11() real ext-real set
b is V11() real ext-real set
|[a,b]| is non empty V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
r is V11() real ext-real set
(2,|[a,b]|,r) is closed bounded convex Element of K6( the carrier of (TOP-REAL 2))
{ b1 where b1 is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2) : |.(b1 - |[a,b]|).| <= r } is set
closed_inside_of_circle (a,b,r) is Element of K6( the carrier of (TOP-REAL 2))
w is Element of the carrier of (Euclid 2)
cl_Ball (w,r) is Element of K6( the carrier of (Euclid 2))
K6( the carrier of (Euclid 2)) is set
a is V11() real ext-real set
b is V11() real ext-real set
|[a,b]| is non empty V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
r is V11() real ext-real set
(2,|[a,b]|,r) is closed bounded Element of K6( the carrier of (TOP-REAL 2))
{ b1 where b1 is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2) : |.(b1 - |[a,b]|).| = r } is set
circle (a,b,r) is Element of K6( the carrier of (TOP-REAL 2))
w is Element of the carrier of (Euclid 2)
Sphere (w,r) is Element of K6( the carrier of (Euclid 2))
K6( the carrier of (Euclid 2)) is set
a is V11() real ext-real set
b is V11() real ext-real set
r is V11() real ext-real set
inside_of_circle (a,b,r) is Element of K6( the carrier of (TOP-REAL 2))
closed_inside_of_circle (a,b,r) is Element of K6( the carrier of (TOP-REAL 2))
w is set
s is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
|[a,b]| is non empty V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
s - |[a,b]| is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- |[a,b]| is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- |[a,b]| is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
- 1 is V11() real ext-real non positive set
(- 1) * |[a,b]| is V16() V21() set
K382((TOP-REAL 2),s,(- |[a,b]|)) is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) is V16() V21() V30(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2)) Element of K6(K7(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2)))
K7(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2)) is V16() set
K6(K7(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2))) is set
K350( the carrier of (TOP-REAL 2), the U7 of (TOP-REAL 2),s,(- |[a,b]|)) is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
s + (- |[a,b]|) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
s - |[a,b]| is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K448(|[a,b]|) is V16() V21() complex-yielding set
K419(s,K448(|[a,b]|)) is V16() V21() set
|.(s - |[a,b]|).| is V11() real ext-real non negative Element of REAL
sqr (s - |[a,b]|) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt ((s - |[a,b]|),(s - |[a,b]|)) is V16() V21() set
Sum (sqr (s - |[a,b]|)) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (s - |[a,b]|))) is V11() real ext-real Element of REAL
a is V11() real ext-real set
b is V11() real ext-real set
r is V11() real ext-real set
inside_of_circle (a,b,r) is Element of K6( the carrier of (TOP-REAL 2))
circle (a,b,r) is Element of K6( the carrier of (TOP-REAL 2))
w is set
s is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
|[a,b]| is non empty V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
s - |[a,b]| is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- |[a,b]| is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- |[a,b]| is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
- 1 is V11() real ext-real non positive set
(- 1) * |[a,b]| is V16() V21() set
K382((TOP-REAL 2),s,(- |[a,b]|)) is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) is V16() V21() V30(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2)) Element of K6(K7(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2)))
K7(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2)) is V16() set
K6(K7(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2))) is set
K350( the carrier of (TOP-REAL 2), the U7 of (TOP-REAL 2),s,(- |[a,b]|)) is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
s + (- |[a,b]|) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
s - |[a,b]| is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K448(|[a,b]|) is V16() V21() complex-yielding set
K419(s,K448(|[a,b]|)) is V16() V21() set
|.(s - |[a,b]|).| is V11() real ext-real non negative Element of REAL
sqr (s - |[a,b]|) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt ((s - |[a,b]|),(s - |[a,b]|)) is V16() V21() set
Sum (sqr (s - |[a,b]|)) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (s - |[a,b]|))) is V11() real ext-real Element of REAL
a is V11() real ext-real set
b is V11() real ext-real set
r is V11() real ext-real set
inside_of_circle (a,b,r) is Element of K6( the carrier of (TOP-REAL 2))
circle (a,b,r) is Element of K6( the carrier of (TOP-REAL 2))
(inside_of_circle (a,b,r)) \/ (circle (a,b,r)) is Element of K6( the carrier of (TOP-REAL 2))
closed_inside_of_circle (a,b,r) is Element of K6( the carrier of (TOP-REAL 2))
|[a,b]| is non empty V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
w is Element of the carrier of (Euclid 2)
cl_Ball (w,r) is Element of K6( the carrier of (Euclid 2))
K6( the carrier of (Euclid 2)) is set
Sphere (w,r) is Element of K6( the carrier of (Euclid 2))
Ball (w,r) is bounded Element of K6( the carrier of (Euclid 2))
a is V11() real ext-real set
(2,(0. (TOP-REAL 2)),a) is closed bounded Element of K6( the carrier of (TOP-REAL 2))
{ b1 where b1 is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2) : |.(b1 - (0. (TOP-REAL 2))).| = a } is set
a ^2 is V11() real ext-real set
a * a is V11() real ext-real set
b is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
b `1 is V11() real ext-real Element of REAL
(b `1) ^2 is V11() real ext-real Element of REAL
(b `1) * (b `1) is V11() real ext-real set
b `2 is V11() real ext-real Element of REAL
(b `2) ^2 is V11() real ext-real Element of REAL
(b `2) * (b `2) is V11() real ext-real set
((b `1) ^2) + ((b `2) ^2) is V11() real ext-real Element of REAL
b - (0. (TOP-REAL 2)) is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- (0. (TOP-REAL 2)) is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- (0. (TOP-REAL 2)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
- 1 is V11() real ext-real non positive set
(- 1) * (0. (TOP-REAL 2)) is V16() V21() set
K382((TOP-REAL 2),b,(- (0. (TOP-REAL 2)))) is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) is V16() V21() V30(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2)) Element of K6(K7(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2)))
K7(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2)) is V16() set
K6(K7(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2))) is set
K350( the carrier of (TOP-REAL 2), the U7 of (TOP-REAL 2),b,(- (0. (TOP-REAL 2)))) is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
b + (- (0. (TOP-REAL 2))) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
b - (0. (TOP-REAL 2)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K448((0. (TOP-REAL 2))) is V16() V21() complex-yielding set
K419(b,K448((0. (TOP-REAL 2)))) is V16() V21() set
|.(b - (0. (TOP-REAL 2))).| is V11() real ext-real non negative Element of REAL
sqr (b - (0. (TOP-REAL 2))) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt ((b - (0. (TOP-REAL 2))),(b - (0. (TOP-REAL 2)))) is V16() V21() set
Sum (sqr (b - (0. (TOP-REAL 2)))) is V11() real ext-real Element of REAL
sqrt (Sum (sqr (b - (0. (TOP-REAL 2))))) is V11() real ext-real Element of REAL
|.b.| is V11() real ext-real non negative Element of REAL
sqr b is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
mlt (b,b) is V16() V21() set
Sum (sqr b) is V11() real ext-real Element of REAL
sqrt (Sum (sqr b)) is V11() real ext-real Element of REAL
a is V11() real ext-real set
b is V11() real ext-real set
r is V11() real ext-real set
closed_inside_of_circle (a,b,r) is Element of K6( the carrier of (TOP-REAL 2))
w is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
s is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
|[a,b]| is non empty V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
t is Element of the carrier of (Euclid 2)
cl_Ball (t,r) is Element of K6( the carrier of (Euclid 2))
K6( the carrier of (Euclid 2)) is set
a is V11() real ext-real set
b is V11() real ext-real set
|[a,b]| is non empty V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
r is V11() real ext-real set
1 - r is V11() real ext-real Element of REAL
- r is V11() real ext-real set
1 + (- r) is V11() real ext-real set
w is V11() real ext-real set
w ^2 is V11() real ext-real set
w * w is V11() real ext-real set
inside_of_circle (a,b,w) is Element of K6( the carrier of (TOP-REAL 2))
circle (a,b,w) is Element of K6( the carrier of (TOP-REAL 2))
s is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
s - |[a,b]| is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- |[a,b]| is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- |[a,b]| is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
- 1 is V11() real ext-real non positive set
(- 1) * |[a,b]| is V16() V21() set
K382((TOP-REAL 2),s,(- |[a,b]|)) is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) is V16() V21() V30(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2)) Element of K6(K7(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2)))
K7(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2)) is V16() set
K6(K7(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2))) is set
K350( the carrier of (TOP-REAL 2), the U7 of (TOP-REAL 2),s,(- |[a,b]|)) is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
s + (- |[a,b]|) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
s - |[a,b]| is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K448(|[a,b]|) is V16() V21() complex-yielding set
K419(s,K448(|[a,b]|)) is V16() V21() set
(1 - r) * s is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(1 - r) * s is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
t is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
t - s is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- s is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- s is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(- 1) * s is V16() V21() set
K382((TOP-REAL 2),t,(- s)) is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K350( the carrier of (TOP-REAL 2), the U7 of (TOP-REAL 2),t,(- s)) is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
t + (- s) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
t - s is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K448(s) is V16() V21() complex-yielding set
K419(t,K448(s)) is V16() V21() set
|((t - s),(s - |[a,b]|))| is V11() real ext-real Element of REAL
2 * |((t - s),(s - |[a,b]|))| is V11() real ext-real Element of REAL
- (2 * |((t - s),(s - |[a,b]|))|) is V11() real ext-real Element of REAL
(2,s,t) is non empty convex Element of K6( the carrier of (TOP-REAL 2))
{ (((1 - b1) * s) + (b1 * t)) where b1 is V11() real ext-real Element of REAL : 0 <= b1 } is set
(2,s,t) /\ (circle (a,b,w)) is Element of K6( the carrier of (TOP-REAL 2))
r * t is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
r * t is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - r) * s) + (r * t) is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K350( the carrier of (TOP-REAL 2), the U7 of (TOP-REAL 2),((1 - r) * s),(r * t)) is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((1 - r) * s) + (r * t) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(2,|[a,b]|,w) is open bounded convex Element of K6( the carrier of (TOP-REAL 2))
{ b1 where b1 is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2) : not w <= |.(b1 - |[a,b]|).| } is set
(2,|[a,b]|,w) is closed bounded Element of K6( the carrier of (TOP-REAL 2))
{ b1 where b1 is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2) : |.(b1 - |[a,b]|).| = w } is set
G is V16() V19( NAT ) V20( REAL ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL 2
S is V16() V19( NAT ) V20( REAL ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL 2
T is V16() V19( NAT ) V20( REAL ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL 2
S - G is V16() V19( NAT ) V20( REAL ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL 2
K448(G) is V16() V21() complex-yielding set
(- 1) * G is V16() V21() set
K419(S,K448(G)) is V16() V21() set
sqr (S - G) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of 2 -tuples_on REAL
mlt ((S - G),(S - G)) is V16() V21() set
Sum (sqr (S - G)) is V11() real ext-real Element of REAL
G - T is V16() V19( NAT ) V20( REAL ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL 2
K448(T) is V16() V21() complex-yielding set
(- 1) * T is V16() V21() set
K419(G,K448(T)) is V16() V21() set
sqr (G - T) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of 2 -tuples_on REAL
mlt ((G - T),(G - T)) is V16() V21() set
Sum (sqr (G - T)) is V11() real ext-real Element of REAL
(Sum (sqr (G - T))) - (w ^2) is V11() real ext-real Element of REAL
- (w ^2) is V11() real ext-real set
(Sum (sqr (G - T))) + (- (w ^2)) is V11() real ext-real set
delta ((Sum (sqr (S - G))),(2 * |((t - s),(s - |[a,b]|))|),((Sum (sqr (G - T))) - (w ^2))) is V11() real ext-real Element of REAL
sqrt (delta ((Sum (sqr (S - G))),(2 * |((t - s),(s - |[a,b]|))|),((Sum (sqr (G - T))) - (w ^2)))) is V11() real ext-real Element of REAL
(- (2 * |((t - s),(s - |[a,b]|))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((t - s),(s - |[a,b]|))|),((Sum (sqr (G - T))) - (w ^2))))) is V11() real ext-real Element of REAL
2 * (Sum (sqr (S - G))) is V11() real ext-real Element of REAL
((- (2 * |((t - s),(s - |[a,b]|))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((t - s),(s - |[a,b]|))|),((Sum (sqr (G - T))) - (w ^2)))))) / (2 * (Sum (sqr (S - G)))) is V11() real ext-real Element of REAL
(2 * (Sum (sqr (S - G)))) " is V11() real ext-real set
((- (2 * |((t - s),(s - |[a,b]|))|)) + (sqrt (delta ((Sum (sqr (S - G))),(2 * |((t - s),(s - |[a,b]|))|),((Sum (sqr (G - T))) - (w ^2)))))) * ((2 * (Sum (sqr (S - G)))) ") is V11() real ext-real set
a is V11() real ext-real set
b is V11() real ext-real set
r is V11() real ext-real set
circle (a,b,r) is Element of K6( the carrier of (TOP-REAL 2))
inside_of_circle (a,b,r) is Element of K6( the carrier of (TOP-REAL 2))
w is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
{w} is non empty V24() set
s is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
LSeg (w,s) is Element of K6( the carrier of (TOP-REAL 2))
{ (((1 - b1) * w) + (b1 * s)) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
(LSeg (w,s)) /\ (circle (a,b,r)) is Element of K6( the carrier of (TOP-REAL 2))
|[a,b]| is non empty V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
t is Element of the carrier of (Euclid 2)
Ball (t,r) is bounded Element of K6( the carrier of (Euclid 2))
K6( the carrier of (Euclid 2)) is set
(2,|[a,b]|,r) is open bounded convex Element of K6( the carrier of (TOP-REAL 2))
{ b1 where b1 is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2) : not r <= |.(b1 - |[a,b]|).| } is set
Sphere (t,r) is Element of K6( the carrier of (Euclid 2))
(2,|[a,b]|,r) is closed bounded Element of K6( the carrier of (TOP-REAL 2))
{ b1 where b1 is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2) : |.(b1 - |[a,b]|).| = r } is set
a is V11() real ext-real set
b is V11() real ext-real set
r is V11() real ext-real set
circle (a,b,r) is Element of K6( the carrier of (TOP-REAL 2))
inside_of_circle (a,b,r) is Element of K6( the carrier of (TOP-REAL 2))
w is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
s is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
LSeg (w,s) is Element of K6( the carrier of (TOP-REAL 2))
{ (((1 - b1) * w) + (b1 * s)) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
{w,s} is non empty V24() set
(LSeg (w,s)) \ {w,s} is Element of K6( the carrier of (TOP-REAL 2))
|[a,b]| is non empty V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
t is Element of the carrier of (Euclid 2)
Sphere (t,r) is Element of K6( the carrier of (Euclid 2))
K6( the carrier of (Euclid 2)) is set
(2,|[a,b]|,r) is closed bounded Element of K6( the carrier of (TOP-REAL 2))
{ b1 where b1 is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2) : |.(b1 - |[a,b]|).| = r } is set
(2,|[a,b]|,r) is open bounded convex Element of K6( the carrier of (TOP-REAL 2))
{ b1 where b1 is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2) : not r <= |.(b1 - |[a,b]|).| } is set
a is V11() real ext-real set
b is V11() real ext-real set
r is V11() real ext-real set
circle (a,b,r) is Element of K6( the carrier of (TOP-REAL 2))
w is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
s is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
LSeg (w,s) is Element of K6( the carrier of (TOP-REAL 2))
{ (((1 - b1) * w) + (b1 * s)) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
(LSeg (w,s)) /\ (circle (a,b,r)) is Element of K6( the carrier of (TOP-REAL 2))
{w,s} is non empty V24() set
|[a,b]| is non empty V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
t is Element of the carrier of (Euclid 2)
Sphere (t,r) is Element of K6( the carrier of (Euclid 2))
K6( the carrier of (Euclid 2)) is set
(2,|[a,b]|,r) is closed bounded Element of K6( the carrier of (TOP-REAL 2))
{ b1 where b1 is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2) : |.(b1 - |[a,b]|).| = r } is set
a is V11() real ext-real set
b is V11() real ext-real set
r is V11() real ext-real set
circle (a,b,r) is Element of K6( the carrier of (TOP-REAL 2))
w is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
s is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(2,w,s) is non empty convex Element of K6( the carrier of (TOP-REAL 2))
{ (((1 - b1) * w) + (b1 * s)) where b1 is V11() real ext-real Element of REAL : 0 <= b1 } is set
(2,w,s) /\ (circle (a,b,r)) is Element of K6( the carrier of (TOP-REAL 2))
{w,s} is non empty V24() set
|[a,b]| is non empty V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
t is Element of the carrier of (Euclid 2)
Sphere (t,r) is Element of K6( the carrier of (Euclid 2))
K6( the carrier of (Euclid 2)) is set
(2,|[a,b]|,r) is closed bounded Element of K6( the carrier of (TOP-REAL 2))
{ b1 where b1 is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2) : |.(b1 - |[a,b]|).| = r } is set
a is V11() real ext-real set
b is V11() real ext-real set
|[a,b]| is non empty V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
r is V11() real ext-real set
circle (a,b,r) is Element of K6( the carrier of (TOP-REAL 2))
closed_inside_of_circle (a,b,r) is Element of K6( the carrier of (TOP-REAL 2))
(2,|[a,b]|,r) is closed bounded Element of K6( the carrier of (TOP-REAL 2))
{ b1 where b1 is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2) : |.(b1 - |[a,b]|).| = r } is set
r ^2 is V11() real ext-real set
r * r is V11() real ext-real set
w is V11() real ext-real set
1 - w is V11() real ext-real Element of REAL
- w is V11() real ext-real set
1 + (- w) is V11() real ext-real set
s is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(1 / 2) * s is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(1 / 2) * s is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
t is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(1 / 2) * t is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(1 / 2) * t is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 / 2) * s) + ((1 / 2) * t) is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) is V16() V21() V30(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2)) Element of K6(K7(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2)))
K7(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2)) is V16() set
K6(K7(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2))) is set
K350( the carrier of (TOP-REAL 2), the U7 of (TOP-REAL 2),((1 / 2) * s),((1 / 2) * t)) is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((1 / 2) * s) + ((1 / 2) * t) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(2,s,t) is non empty convex Element of K6( the carrier of (TOP-REAL 2))
{ (((1 - b1) * s) + (b1 * t)) where b1 is V11() real ext-real Element of REAL : 0 <= b1 } is set
(2,s,t) /\ (circle (a,b,r)) is Element of K6( the carrier of (TOP-REAL 2))
t - (((1 / 2) * s) + ((1 / 2) * t)) is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- (((1 / 2) * s) + ((1 / 2) * t)) is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- (((1 / 2) * s) + ((1 / 2) * t)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
- 1 is V11() real ext-real non positive set
(- 1) * (((1 / 2) * s) + ((1 / 2) * t)) is V16() V21() set
K382((TOP-REAL 2),t,(- (((1 / 2) * s) + ((1 / 2) * t)))) is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K350( the carrier of (TOP-REAL 2), the U7 of (TOP-REAL 2),t,(- (((1 / 2) * s) + ((1 / 2) * t)))) is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
t + (- (((1 / 2) * s) + ((1 / 2) * t))) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
t - (((1 / 2) * s) + ((1 / 2) * t)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K448((((1 / 2) * s) + ((1 / 2) * t))) is V16() V21() complex-yielding set
K419(t,K448((((1 / 2) * s) + ((1 / 2) * t)))) is V16() V21() set
(((1 / 2) * s) + ((1 / 2) * t)) - |[a,b]| is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- |[a,b]| is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- |[a,b]| is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(- 1) * |[a,b]| is V16() V21() set
K382((TOP-REAL 2),(((1 / 2) * s) + ((1 / 2) * t)),(- |[a,b]|)) is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K350( the carrier of (TOP-REAL 2), the U7 of (TOP-REAL 2),(((1 / 2) * s) + ((1 / 2) * t)),(- |[a,b]|)) is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(((1 / 2) * s) + ((1 / 2) * t)) + (- |[a,b]|) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((1 / 2) * s) + ((1 / 2) * t)) - |[a,b]| is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
K448(|[a,b]|) is V16() V21() complex-yielding set
K419((((1 / 2) * s) + ((1 / 2) * t)),K448(|[a,b]|)) is V16() V21() set
|((t - (((1 / 2) * s) + ((1 / 2) * t))),((((1 / 2) * s) + ((1 / 2) * t)) - |[a,b]|))| is V11() real ext-real Element of REAL
2 * |((t - (((1 / 2) * s) + ((1 / 2) * t))),((((1 / 2) * s) + ((1 / 2) * t)) - |[a,b]|))| is V11() real ext-real Element of REAL
- (2 * |((t - (((1 / 2) * s) + ((1 / 2) * t))),((((1 / 2) * s) + ((1 / 2) * t)) - |[a,b]|))|) is V11() real ext-real Element of REAL
(1 - w) * (((1 / 2) * s) + ((1 / 2) * t)) is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(1 - w) * (((1 / 2) * s) + ((1 / 2) * t)) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
w * t is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
w * t is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - w) * (((1 / 2) * s) + ((1 / 2) * t))) + (w * t) is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K350( the carrier of (TOP-REAL 2), the U7 of (TOP-REAL 2),((1 - w) * (((1 / 2) * s) + ((1 / 2) * t))),(w * t)) is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((1 - w) * (((1 / 2) * s) + ((1 / 2) * t))) + (w * t) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
G is Element of the carrier of (Euclid 2)
cl_Ball (G,r) is Element of K6( the carrier of (Euclid 2))
K6( the carrier of (Euclid 2)) is set
(2,|[a,b]|,r) is closed bounded convex Element of K6( the carrier of (TOP-REAL 2))
{ b1 where b1 is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2) : |.(b1 - |[a,b]|).| <= r } is set
Sphere (G,r) is Element of K6( the carrier of (Euclid 2))
S is V16() V19( NAT ) V20( REAL ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL 2
T is V16() V19( NAT ) V20( REAL ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL 2
Y is V16() V19( NAT ) V20( REAL ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL 2
T - S is V16() V19( NAT ) V20( REAL ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL 2
K448(S) is V16() V21() complex-yielding set
(- 1) * S is V16() V21() set
K419(T,K448(S)) is V16() V21() set
sqr (T - S) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of 2 -tuples_on REAL
mlt ((T - S),(T - S)) is V16() V21() set
Sum (sqr (T - S)) is V11() real ext-real Element of REAL
S - Y is V16() V19( NAT ) V20( REAL ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL 2
K448(Y) is V16() V21() complex-yielding set
(- 1) * Y is V16() V21() set
K419(S,K448(Y)) is V16() V21() set
sqr (S - Y) is V16() V19( NAT ) V20( REAL ) V21() V37() FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of 2 -tuples_on REAL
mlt ((S - Y),(S - Y)) is V16() V21() set
Sum (sqr (S - Y)) is V11() real ext-real Element of REAL
(Sum (sqr (S - Y))) - (r ^2) is V11() real ext-real Element of REAL
- (r ^2) is V11() real ext-real set
(Sum (sqr (S - Y))) + (- (r ^2)) is V11() real ext-real set
delta ((Sum (sqr (T - S))),(2 * |((t - (((1 / 2) * s) + ((1 / 2) * t))),((((1 / 2) * s) + ((1 / 2) * t)) - |[a,b]|))|),((Sum (sqr (S - Y))) - (r ^2))) is V11() real ext-real Element of REAL
sqrt (delta ((Sum (sqr (T - S))),(2 * |((t - (((1 / 2) * s) + ((1 / 2) * t))),((((1 / 2) * s) + ((1 / 2) * t)) - |[a,b]|))|),((Sum (sqr (S - Y))) - (r ^2)))) is V11() real ext-real Element of REAL
(- (2 * |((t - (((1 / 2) * s) + ((1 / 2) * t))),((((1 / 2) * s) + ((1 / 2) * t)) - |[a,b]|))|)) + (sqrt (delta ((Sum (sqr (T - S))),(2 * |((t - (((1 / 2) * s) + ((1 / 2) * t))),((((1 / 2) * s) + ((1 / 2) * t)) - |[a,b]|))|),((Sum (sqr (S - Y))) - (r ^2))))) is V11() real ext-real Element of REAL
2 * (Sum (sqr (T - S))) is V11() real ext-real Element of REAL
((- (2 * |((t - (((1 / 2) * s) + ((1 / 2) * t))),((((1 / 2) * s) + ((1 / 2) * t)) - |[a,b]|))|)) + (sqrt (delta ((Sum (sqr (T - S))),(2 * |((t - (((1 / 2) * s) + ((1 / 2) * t))),((((1 / 2) * s) + ((1 / 2) * t)) - |[a,b]|))|),((Sum (sqr (S - Y))) - (r ^2)))))) / (2 * (Sum (sqr (T - S)))) is V11() real ext-real Element of REAL
(2 * (Sum (sqr (T - S)))) " is V11() real ext-real set
((- (2 * |((t - (((1 / 2) * s) + ((1 / 2) * t))),((((1 / 2) * s) + ((1 / 2) * t)) - |[a,b]|))|)) + (sqrt (delta ((Sum (sqr (T - S))),(2 * |((t - (((1 / 2) * s) + ((1 / 2) * t))),((((1 / 2) * s) + ((1 / 2) * t)) - |[a,b]|))|),((Sum (sqr (S - Y))) - (r ^2)))))) * ((2 * (Sum (sqr (T - S)))) ") is V11() real ext-real set
a is V11() real ext-real set
b is V11() real ext-real set
r is V11() real ext-real set
inside_of_circle (a,b,r) is Element of K6( the carrier of (TOP-REAL 2))
|[a,b]| is non empty V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
{ b1 where b1 is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2) : not r <= |.(b1 - |[a,b]|).| } is set
closed_inside_of_circle (a,b,r) is Element of K6( the carrier of (TOP-REAL 2))
|[a,b]| is non empty V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
{ b1 where b1 is V16() V19( NAT ) V21() V37() V44(2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL 2) : |.(b1 - |[a,b]|).| <= r } is set