:: BROUWER2 semantic presentation

REAL is complex-membered ext-real-membered real-membered V153() set
NAT is V12() ordinal V32() cardinal limit_cardinal complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V153() Element of K19(REAL)
K19(REAL) is non empty set
COMPLEX is complex-membered V153() set
RAT is complex-membered ext-real-membered real-membered rational-membered V153() set
INT is complex-membered ext-real-membered real-membered rational-membered integer-membered V153() set
K20(COMPLEX,COMPLEX) is Relation-like V137() set
K19(K20(COMPLEX,COMPLEX)) is non empty set
K20(K20(COMPLEX,COMPLEX),COMPLEX) is Relation-like V137() set
K19(K20(K20(COMPLEX,COMPLEX),COMPLEX)) is non empty set
K20(REAL,REAL) is Relation-like V137() V138() V139() set
K19(K20(REAL,REAL)) is non empty set
K20(K20(REAL,REAL),REAL) is Relation-like V137() V138() V139() set
K19(K20(K20(REAL,REAL),REAL)) is non empty set
K20(RAT,RAT) is Relation-like RAT -valued V137() V138() V139() set
K19(K20(RAT,RAT)) is non empty set
K20(K20(RAT,RAT),RAT) is Relation-like RAT -valued V137() V138() V139() set
K19(K20(K20(RAT,RAT),RAT)) is non empty set
K20(INT,INT) is Relation-like RAT -valued INT -valued V137() V138() V139() set
K19(K20(INT,INT)) is non empty set
K20(K20(INT,INT),INT) is Relation-like RAT -valued INT -valued V137() V138() V139() set
K19(K20(K20(INT,INT),INT)) is non empty set
K20(NAT,NAT) is Relation-like RAT -valued INT -valued V137() V138() V139() V140() set
K20(K20(NAT,NAT),NAT) is Relation-like RAT -valued INT -valued V137() V138() V139() V140() set
K19(K20(K20(NAT,NAT),NAT)) is non empty set
omega is V12() ordinal V32() cardinal limit_cardinal complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V153() set
K19(omega) is non empty V12() V32() set
1 is non empty V21() ordinal natural real V30() V31() V32() cardinal ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered Element of NAT
K20(1,1) is Relation-like RAT -valued INT -valued non empty V32() V137() V138() V139() V140() set
K19(K20(1,1)) is non empty V32() V36() set
K20(K20(1,1),1) is Relation-like RAT -valued INT -valued non empty V32() V137() V138() V139() V140() set
K19(K20(K20(1,1),1)) is non empty V32() V36() set
K20(K20(1,1),REAL) is Relation-like V137() V138() V139() set
K19(K20(K20(1,1),REAL)) is non empty set
2 is non empty V21() ordinal natural real V30() V31() V32() cardinal ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered Element of NAT
K20(2,2) is Relation-like RAT -valued INT -valued non empty V32() V137() V138() V139() V140() set
K20(K20(2,2),REAL) is Relation-like V137() V138() V139() set
K19(K20(K20(2,2),REAL)) is non empty set
K19(NAT) is non empty V12() V32() set
K383() is non empty V93() L9()
the carrier of K383() is non empty set
K388() is non empty L9()
K389() is non empty V93() M13(K388())
K390() is non empty V93() V115() V175() M16(K388(),K389())
K392() is non empty V93() V115() V117() V119() L9()
K393() is non empty V93() V115() V175() M13(K392())
{} is Relation-like non-empty empty-yielding RAT -valued Function-like one-to-one constant functional empty V21() ordinal natural real V32() V33() V36() cardinal {} -element ext-real non positive non negative V137() V138() V139() V140() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V153() Function-yielding V275() complex-functions-membered ext-real-functions-membered real-functions-membered rational-functions-membered integer-functions-membered natural-functions-membered complex-functions-valued ext-real-functions-valued real-functions-valued rational-functions-valued integer-functions-valued natural-functions-valued set
{{},1} is non empty V32() V36() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered set
TOP-REAL 2 is non empty V46() V90() V91() V160() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V188() TopSpace-like T_0 T_1 T_2 strict add-continuous Mult-continuous V310() V311() finite-dimensional RLTopStruct
the carrier of (TOP-REAL 2) is functional non empty V12() complex-functions-membered ext-real-functions-membered real-functions-membered set
I[01] is non empty strict TopSpace-like real-membered TopStruct
the carrier of I[01] is non empty complex-membered ext-real-membered real-membered set
RealSpace is strict real-membered MetrStruct
R^1 is non empty strict TopSpace-like real-membered TopStruct
the carrier of R^1 is non empty complex-membered ext-real-membered real-membered set
K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)) is Relation-like non empty set
K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2))) is non empty set
I[01] is non empty strict TopSpace-like real-membered SubSpace of R^1
K706(I[01],I[01]) is non empty strict TopSpace-like TopStruct
the carrier of K706(I[01],I[01]) is non empty set
K878() is non empty strict TopSpace-like real-membered V308() SubSpace of R^1
the carrier of K878() is non empty complex-membered ext-real-membered real-membered set
K19( the carrier of K878()) is non empty set
K19(K19( the carrier of K878())) is non empty set
Tunit_circle 2 is TopSpace-like T_0 T_1 T_2 V310() V311() SubSpace of TOP-REAL 2
the carrier of (Tunit_circle 2) is functional complex-functions-membered ext-real-functions-membered real-functions-membered set
K20( the carrier of K878(), the carrier of (Tunit_circle 2)) is Relation-like set
K19(K20( the carrier of K878(), the carrier of (Tunit_circle 2))) is non empty set
CircleMap is Relation-like the carrier of K878() -defined the carrier of (Tunit_circle 2) -valued Function-like quasi_total Function-yielding V275() complex-functions-valued ext-real-functions-valued real-functions-valued Element of K19(K20( the carrier of K878(), the carrier of (Tunit_circle 2)))
c[10] is Relation-like Function-like V137() V138() V139() Element of the carrier of (Tunit_circle 2)
Topen_unit_circle c[10] is strict TopSpace-like T_0 T_1 T_2 V310() V311() SubSpace of Tunit_circle 2
the carrier of (Topen_unit_circle c[10]) is functional complex-functions-membered ext-real-functions-membered real-functions-membered set
0 is Relation-like non-empty empty-yielding RAT -valued Function-like one-to-one constant functional empty V21() ordinal natural real V30() V31() V32() V33() V36() cardinal {} -element ext-real non positive non negative V137() V138() V139() V140() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V153() Function-yielding V275() complex-functions-membered ext-real-functions-membered real-functions-membered rational-functions-membered integer-functions-membered natural-functions-membered complex-functions-valued ext-real-functions-valued real-functions-valued rational-functions-valued integer-functions-valued natural-functions-valued Element of NAT
K872(0,1) is complex-membered ext-real-membered real-membered Element of K19(REAL)
R^1 K872(0,1) is complex-membered ext-real-membered real-membered Element of K19( the carrier of K878())
K878() | (R^1 K872(0,1)) is strict TopSpace-like real-membered SubSpace of K878()
the carrier of (K878() | (R^1 K872(0,1))) is complex-membered ext-real-membered real-membered set
K20( the carrier of (Topen_unit_circle c[10]), the carrier of (K878() | (R^1 K872(0,1)))) is Relation-like V137() V138() V139() set
K19(K20( the carrier of (Topen_unit_circle c[10]), the carrier of (K878() | (R^1 K872(0,1))))) is non empty set
c[-10] is Relation-like Function-like V137() V138() V139() Element of the carrier of (Tunit_circle 2)
Topen_unit_circle c[-10] is strict TopSpace-like T_0 T_1 T_2 V310() V311() SubSpace of Tunit_circle 2
the carrier of (Topen_unit_circle c[-10]) is functional complex-functions-membered ext-real-functions-membered real-functions-membered set
1 / 2 is non empty V21() real ext-real positive non negative Element of REAL
2 " is non empty V21() real ext-real positive non negative set
1 * (2 ") is non empty V21() real ext-real positive non negative set
3 is non empty V21() ordinal natural real V30() V31() V32() cardinal ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered Element of NAT
3 / 2 is non empty V21() real ext-real positive non negative Element of REAL
3 * (2 ") is non empty V21() real ext-real positive non negative set
K872((1 / 2),(3 / 2)) is complex-membered ext-real-membered real-membered Element of K19(REAL)
R^1 K872((1 / 2),(3 / 2)) is complex-membered ext-real-membered real-membered Element of K19( the carrier of K878())
K878() | (R^1 K872((1 / 2),(3 / 2))) is strict TopSpace-like real-membered SubSpace of K878()
the carrier of (K878() | (R^1 K872((1 / 2),(3 / 2)))) is complex-membered ext-real-membered real-membered set
K20( the carrier of (Topen_unit_circle c[-10]), the carrier of (K878() | (R^1 K872((1 / 2),(3 / 2))))) is Relation-like V137() V138() V139() set
K19(K20( the carrier of (Topen_unit_circle c[-10]), the carrier of (K878() | (R^1 K872((1 / 2),(3 / 2)))))) is non empty set
K20(NAT,REAL) is Relation-like V137() V138() V139() set
K19(K20(NAT,REAL)) is non empty set
K20(COMPLEX,REAL) is Relation-like V137() V138() V139() set
K19(K20(COMPLEX,REAL)) is non empty set
REAL 0 is functional non empty V78() complex-functions-membered ext-real-functions-membered real-functions-membered M10( REAL )
TOP-REAL 0 is non empty V46() V47() 1 -element V90() V91() V160() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V188() TopSpace-like T_0 T_1 T_2 strict add-continuous Mult-continuous compact real-membered V310() V311() finite-dimensional RLTopStruct
0. (TOP-REAL 0) is Relation-like non-empty empty-yielding RAT -valued Function-like one-to-one constant functional empty V21() ordinal natural real V32() V33() V36() cardinal 0 -element V48( TOP-REAL 0) V76() ext-real non positive non negative V137() V138() V139() V140() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V153() Function-yielding V275() complex-functions-membered ext-real-functions-membered real-functions-membered rational-functions-membered integer-functions-membered natural-functions-membered complex-functions-valued ext-real-functions-valued real-functions-valued rational-functions-valued integer-functions-valued natural-functions-valued Element of the carrier of (TOP-REAL 0)
the carrier of (TOP-REAL 0) is functional non empty V12() V32() 1 -element complex-membered ext-real-membered real-membered complex-functions-membered ext-real-functions-membered real-functions-membered set
the ZeroF of (TOP-REAL 0) is Relation-like non-empty empty-yielding RAT -valued Function-like one-to-one constant functional empty V21() ordinal natural real V32() V33() V36() cardinal 0 -element V76() ext-real non positive non negative V137() V138() V139() V140() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V153() Function-yielding V275() complex-functions-membered ext-real-functions-membered real-functions-membered rational-functions-membered integer-functions-membered natural-functions-membered complex-functions-valued ext-real-functions-valued real-functions-valued rational-functions-valued integer-functions-valued natural-functions-valued Element of the carrier of (TOP-REAL 0)
{(0. (TOP-REAL 0))} is functional non empty V12() V32() V36() 1 -element complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered complex-functions-membered set
- 1 is non empty V21() real ext-real non positive negative Element of REAL
n is V21() ordinal natural real V32() cardinal ext-real non negative set
TOP-REAL n is non empty V90() V91() V160() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V188() TopSpace-like T_0 T_1 T_2 strict add-continuous Mult-continuous V310() V311() finite-dimensional RLTopStruct
the carrier of (TOP-REAL n) is functional non empty complex-functions-membered ext-real-functions-membered real-functions-membered set
T is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
cB is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
cB - T is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
- T is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K364(T) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K246((TOP-REAL n),cB,(- T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
the U6 of (TOP-REAL n) is Relation-like K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)) -defined the carrier of (TOP-REAL n) -valued Function-like non empty V14(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n))) quasi_total Function-yielding V275() complex-functions-valued ext-real-functions-valued real-functions-valued Element of K19(K20(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)), the carrier of (TOP-REAL n)))
K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)) is Relation-like non empty set
K20(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)), the carrier of (TOP-REAL n)) is Relation-like non empty set
K19(K20(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)), the carrier of (TOP-REAL n))) is non empty set
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),cB,(- T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362(cB,(- T)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K366(cB,T) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
S is V21() real ext-real set
1 - S is V21() real ext-real Element of REAL
- S is V21() real ext-real set
1 + (- S) is V21() real ext-real set
(1 - S) * T is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368(T,(1 - S)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
S * cB is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368(cB,S) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
((1 - S) * T) + (S * cB) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),((1 - S) * T),(S * cB)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362(((1 - S) * T),(S * cB)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
(((1 - S) * T) + (S * cB)) - T is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K246((TOP-REAL n),(((1 - S) * T) + (S * cB)),(- T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),(((1 - S) * T) + (S * cB)),(- T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362((((1 - S) * T) + (S * cB)),(- T)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K366((((1 - S) * T) + (S * cB)),T) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
S * (cB - T) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368((cB - T),S) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
((1 - S) * T) - T is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K246((TOP-REAL n),((1 - S) * T),(- T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),((1 - S) * T),(- T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362(((1 - S) * T),(- T)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K366(((1 - S) * T),T) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
(S * cB) + (((1 - S) * T) - T) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),(S * cB),(((1 - S) * T) - T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362((S * cB),(((1 - S) * T) - T)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
1 * T is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368(T,1) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
S * T is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368(T,S) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
(1 * T) - (S * T) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
- (S * T) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K364((S * T)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K246((TOP-REAL n),(1 * T),(- (S * T))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),(1 * T),(- (S * T))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362((1 * T),(- (S * T))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K366((1 * T),(S * T)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
((1 * T) - (S * T)) - T is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K246((TOP-REAL n),((1 * T) - (S * T)),(- T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),((1 * T) - (S * T)),(- T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362(((1 * T) - (S * T)),(- T)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K366(((1 * T) - (S * T)),T) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
(S * cB) + (((1 * T) - (S * T)) - T) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),(S * cB),(((1 * T) - (S * T)) - T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362((S * cB),(((1 * T) - (S * T)) - T)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
T - (S * T) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K246((TOP-REAL n),T,(- (S * T))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),T,(- (S * T))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362(T,(- (S * T))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K366(T,(S * T)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
(T - (S * T)) - T is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K246((TOP-REAL n),(T - (S * T)),(- T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),(T - (S * T)),(- T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362((T - (S * T)),(- T)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K366((T - (S * T)),T) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
(S * cB) + ((T - (S * T)) - T) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),(S * cB),((T - (S * T)) - T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362((S * cB),((T - (S * T)) - T)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
T + (- (S * T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
(T + (- (S * T))) + (- T) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),(T + (- (S * T))),(- T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362((T + (- (S * T))),(- T)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
(S * cB) + ((T + (- (S * T))) + (- T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),(S * cB),((T + (- (S * T))) + (- T))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362((S * cB),((T + (- (S * T))) + (- T))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
T + (- T) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),T,(- T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362(T,(- T)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
(T + (- T)) + (- (S * T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),(T + (- T)),(- (S * T))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362((T + (- T)),(- (S * T))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
(S * cB) + ((T + (- T)) + (- (S * T))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),(S * cB),((T + (- T)) + (- (S * T)))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362((S * cB),((T + (- T)) + (- (S * T)))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
T - T is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K246((TOP-REAL n),T,(- T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K366(T,T) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
(T - T) - (S * T) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K246((TOP-REAL n),(T - T),(- (S * T))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),(T - T),(- (S * T))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362((T - T),(- (S * T))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K366((T - T),(S * T)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
(S * cB) + ((T - T) - (S * T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),(S * cB),((T - T) - (S * T))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362((S * cB),((T - T) - (S * T))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
0. (TOP-REAL n) is Relation-like Function-like n -element V48( TOP-REAL n) V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
the ZeroF of (TOP-REAL n) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
(0. (TOP-REAL n)) - (S * T) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K246((TOP-REAL n),(0. (TOP-REAL n)),(- (S * T))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),(0. (TOP-REAL n)),(- (S * T))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362((0. (TOP-REAL n)),(- (S * T))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K366((0. (TOP-REAL n)),(S * T)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
(S * cB) + ((0. (TOP-REAL n)) - (S * T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),(S * cB),((0. (TOP-REAL n)) - (S * T))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362((S * cB),((0. (TOP-REAL n)) - (S * T))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
(S * cB) - (S * T) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K246((TOP-REAL n),(S * cB),(- (S * T))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),(S * cB),(- (S * T))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362((S * cB),(- (S * T))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K366((S * cB),(S * T)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
n is V21() ordinal natural real V32() cardinal ext-real non negative set
TOP-REAL n is non empty V90() V91() V160() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V188() TopSpace-like T_0 T_1 T_2 strict add-continuous Mult-continuous V310() V311() finite-dimensional RLTopStruct
the carrier of (TOP-REAL n) is functional non empty complex-functions-membered ext-real-functions-membered real-functions-membered set
0. (TOP-REAL n) is Relation-like Function-like n -element V48( TOP-REAL n) V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
the ZeroF of (TOP-REAL n) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
T is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
halfline ((0. (TOP-REAL n)),T) is functional closed complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
K19( the carrier of (TOP-REAL n)) is non empty set
{ (((1 - b₁) * (0. (TOP-REAL n))) + (b₁ * T)) where b₁ is V21() real ext-real Element of REAL : 0 <= b₁ } is set
cB is V21() real ext-real set
cB * T is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368(T,cB) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
1 - cB is V21() real ext-real Element of REAL
- cB is V21() real ext-real set
1 + (- cB) is V21() real ext-real set
(1 - cB) * (0. (TOP-REAL n)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368((0. (TOP-REAL n)),(1 - cB)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
(0. (TOP-REAL n)) + (cB * T) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
the U6 of (TOP-REAL n) is Relation-like K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)) -defined the carrier of (TOP-REAL n) -valued Function-like non empty V14(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n))) quasi_total Function-yielding V275() complex-functions-valued ext-real-functions-valued real-functions-valued Element of K19(K20(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)), the carrier of (TOP-REAL n)))
K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)) is Relation-like non empty set
K20(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)), the carrier of (TOP-REAL n)) is Relation-like non empty set
K19(K20(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)), the carrier of (TOP-REAL n))) is non empty set
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),(0. (TOP-REAL n)),(cB * T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362((0. (TOP-REAL n)),(cB * T)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
n is V21() ordinal natural real V32() cardinal ext-real non negative set
TOP-REAL n is non empty V90() V91() V160() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V188() TopSpace-like T_0 T_1 T_2 strict add-continuous Mult-continuous V310() V311() finite-dimensional RLTopStruct
the carrier of (TOP-REAL n) is functional non empty complex-functions-membered ext-real-functions-membered real-functions-membered set
T is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
cB is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
cB - T is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
- T is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K364(T) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K246((TOP-REAL n),cB,(- T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
the U6 of (TOP-REAL n) is Relation-like K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)) -defined the carrier of (TOP-REAL n) -valued Function-like non empty V14(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n))) quasi_total Function-yielding V275() complex-functions-valued ext-real-functions-valued real-functions-valued Element of K19(K20(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)), the carrier of (TOP-REAL n)))
K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)) is Relation-like non empty set
K20(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)), the carrier of (TOP-REAL n)) is Relation-like non empty set
K19(K20(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)), the carrier of (TOP-REAL n))) is non empty set
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),cB,(- T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362(cB,(- T)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K366(cB,T) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
S is V21() real ext-real set
1 - S is V21() real ext-real Element of REAL
- S is V21() real ext-real set
1 + (- S) is V21() real ext-real set
(1 - S) * T is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368(T,(1 - S)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
S * cB is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368(cB,S) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
((1 - S) * T) + (S * cB) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),((1 - S) * T),(S * cB)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362(((1 - S) * T),(S * cB)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
S * (cB - T) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368((cB - T),S) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
T + (S * (cB - T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),T,(S * (cB - T))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362(T,(S * (cB - T))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
(((1 - S) * T) + (S * cB)) - T is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K246((TOP-REAL n),(((1 - S) * T) + (S * cB)),(- T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),(((1 - S) * T) + (S * cB)),(- T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362((((1 - S) * T) + (S * cB)),(- T)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K366((((1 - S) * T) + (S * cB)),T) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
((((1 - S) * T) + (S * cB)) - T) + T is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),((((1 - S) * T) + (S * cB)) - T),T) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362(((((1 - S) * T) + (S * cB)) - T),T) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
T - T is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K246((TOP-REAL n),T,(- T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),T,(- T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362(T,(- T)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K366(T,T) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
(((1 - S) * T) + (S * cB)) - (T - T) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
- (T - T) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K364((T - T)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K246((TOP-REAL n),(((1 - S) * T) + (S * cB)),(- (T - T))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),(((1 - S) * T) + (S * cB)),(- (T - T))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362((((1 - S) * T) + (S * cB)),(- (T - T))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K366((((1 - S) * T) + (S * cB)),(T - T)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
0. (TOP-REAL n) is Relation-like Function-like n -element V48( TOP-REAL n) V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
the ZeroF of (TOP-REAL n) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
(((1 - S) * T) + (S * cB)) - (0. (TOP-REAL n)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
- (0. (TOP-REAL n)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K364((0. (TOP-REAL n))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K246((TOP-REAL n),(((1 - S) * T) + (S * cB)),(- (0. (TOP-REAL n)))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),(((1 - S) * T) + (S * cB)),(- (0. (TOP-REAL n)))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362((((1 - S) * T) + (S * cB)),(- (0. (TOP-REAL n)))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K366((((1 - S) * T) + (S * cB)),(0. (TOP-REAL n))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
n is V21() ordinal natural real V32() cardinal ext-real non negative set
TOP-REAL n is non empty V90() V91() V160() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V188() TopSpace-like T_0 T_1 T_2 strict add-continuous Mult-continuous V310() V311() finite-dimensional RLTopStruct
the carrier of (TOP-REAL n) is functional non empty complex-functions-membered ext-real-functions-membered real-functions-membered set
T is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
cB is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
T - cB is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
- cB is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K364(cB) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K246((TOP-REAL n),T,(- cB)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
the U6 of (TOP-REAL n) is Relation-like K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)) -defined the carrier of (TOP-REAL n) -valued Function-like non empty V14(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n))) quasi_total Function-yielding V275() complex-functions-valued ext-real-functions-valued real-functions-valued Element of K19(K20(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)), the carrier of (TOP-REAL n)))
K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)) is Relation-like non empty set
K20(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)), the carrier of (TOP-REAL n)) is Relation-like non empty set
K19(K20(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)), the carrier of (TOP-REAL n))) is non empty set
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),T,(- cB)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362(T,(- cB)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K366(T,cB) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
|.(T - cB).| is V21() real ext-real non negative Element of REAL
S is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
halfline (cB,S) is functional closed complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
K19( the carrier of (TOP-REAL n)) is non empty set
{ (((1 - b₁) * cB) + (b₁ * S)) where b₁ is V21() real ext-real Element of REAL : 0 <= b₁ } is set
s is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
s - cB is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K246((TOP-REAL n),s,(- cB)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),s,(- cB)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362(s,(- cB)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K366(s,cB) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
|.(s - cB).| is V21() real ext-real non negative Element of REAL
S - cB is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K246((TOP-REAL n),S,(- cB)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),S,(- cB)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362(S,(- cB)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K366(S,cB) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
|.(S - cB).| is V21() real ext-real non negative Element of REAL
Ts is V21() real ext-real set
1 - Ts is V21() real ext-real Element of REAL
- Ts is V21() real ext-real set
1 + (- Ts) is V21() real ext-real set
(1 - Ts) * cB is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368(cB,(1 - Ts)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
Ts * S is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368(S,Ts) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
((1 - Ts) * cB) + (Ts * S) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),((1 - Ts) * cB),(Ts * S)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362(((1 - Ts) * cB),(Ts * S)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
abs Ts is V21() real ext-real Element of REAL
Ts * (S - cB) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368((S - cB),Ts) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
(abs Ts) * |.(S - cB).| is V21() real ext-real Element of REAL
F is V21() real ext-real set
1 - F is V21() real ext-real Element of REAL
- F is V21() real ext-real set
1 + (- F) is V21() real ext-real set
(1 - F) * cB is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368(cB,(1 - F)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
F * S is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368(S,F) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
((1 - F) * cB) + (F * S) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),((1 - F) * cB),(F * S)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362(((1 - F) * cB),(F * S)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
F * (S - cB) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368((S - cB),F) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
abs F is V21() real ext-real Element of REAL
(abs F) * |.(S - cB).| is V21() real ext-real Element of REAL
{cB} is functional non empty V12() V32() 1 -element closed compact complex-functions-membered ext-real-functions-membered real-functions-membered affinely-independent Element of K19( the carrier of (TOP-REAL n))
n is V21() ordinal natural real V32() cardinal ext-real non negative set
TOP-REAL n is non empty V90() V91() V160() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V188() TopSpace-like T_0 T_1 T_2 strict add-continuous Mult-continuous V310() V311() finite-dimensional RLTopStruct
the carrier of (TOP-REAL n) is functional non empty complex-functions-membered ext-real-functions-membered real-functions-membered set
K19( the carrier of (TOP-REAL n)) is non empty set
Euclid n is non empty strict Reflexive discerning V65() triangle V310() V311() MetrStruct
the carrier of (Euclid n) is functional non empty complex-functions-membered ext-real-functions-membered real-functions-membered set
T is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
cB is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
halfline (T,cB) is functional closed complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
{ (((1 - b₁) * T) + (b₁ * cB)) where b₁ is V21() real ext-real Element of REAL : 0 <= b₁ } is set
s is functional complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
s /\ (halfline (T,cB)) is functional complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
Fr s is functional closed complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
(Fr s) /\ (halfline (T,cB)) is functional closed complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
A is Relation-like Function-like V137() V138() V139() Element of the carrier of (Euclid n)
FR is Relation-like Function-like V137() V138() V139() Element of the carrier of (Euclid n)
dist (A,FR) is V21() real ext-real non negative Element of REAL
K19( the carrier of (Euclid n)) is non empty set
dist (FR,A) is V21() real ext-real non negative Element of REAL
cB - T is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
- T is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K364(T) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K246((TOP-REAL n),cB,(- T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
the U6 of (TOP-REAL n) is Relation-like K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)) -defined the carrier of (TOP-REAL n) -valued Function-like non empty V14(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n))) quasi_total Function-yielding V275() complex-functions-valued ext-real-functions-valued real-functions-valued Element of K19(K20(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)), the carrier of (TOP-REAL n)))
K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)) is Relation-like non empty set
K20(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)), the carrier of (TOP-REAL n)) is Relation-like non empty set
K19(K20(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)), the carrier of (TOP-REAL n))) is non empty set
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),cB,(- T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362(cB,(- T)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K366(cB,T) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
|.(cB - T).| is V21() real ext-real non negative Element of REAL
F is functional bounded complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (Euclid n))
diameter F is V21() real ext-real Element of REAL
{ b₁ where b₁ is V21() real ext-real Element of REAL : ( ((1 - b₁) * T) + (b₁ * cB) in F & {} <= b₁ ) } is set
(diameter F) + 1 is V21() real ext-real Element of REAL
h is set
H is V21() real ext-real Element of REAL
1 - H is V21() real ext-real Element of REAL
- H is V21() real ext-real set
1 + (- H) is V21() real ext-real set
(1 - H) * T is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368(T,(1 - H)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
H * cB is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368(cB,H) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
((1 - H) * T) + (H * cB) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),((1 - H) * T),(H * cB)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362(((1 - H) * T),(H * cB)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
1 * T is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368(T,1) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
{} * cB is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368(cB,{}) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
0. (TOP-REAL n) is Relation-like Function-like n -element V48( TOP-REAL n) V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
the ZeroF of (TOP-REAL n) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
1 - {} is non empty V21() real ext-real positive non negative Element of REAL
- {} is Relation-like non-empty empty-yielding RAT -valued Function-like one-to-one constant functional empty V21() ordinal natural real V32() V33() V36() cardinal {} -element ext-real non positive non negative V137() V138() V139() V140() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V153() Function-yielding V275() complex-functions-membered ext-real-functions-membered real-functions-membered rational-functions-membered integer-functions-membered natural-functions-membered complex-functions-valued ext-real-functions-valued real-functions-valued rational-functions-valued integer-functions-valued natural-functions-valued set
1 + (- {}) is non empty V21() ordinal natural real V32() cardinal ext-real positive non negative set
(1 - {}) * T is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368(T,(1 - {})) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
((1 - {}) * T) + ({} * cB) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),((1 - {}) * T),({} * cB)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362(((1 - {}) * T),({} * cB)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
(diameter F) + {} is V21() real ext-real Element of REAL
H is ext-real set
h is non empty complex-membered ext-real-membered real-membered set
hfh is V21() real ext-real Element of REAL
1 - hfh is V21() real ext-real Element of REAL
- hfh is V21() real ext-real set
1 + (- hfh) is V21() real ext-real set
(1 - hfh) * T is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368(T,(1 - hfh)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
hfh * cB is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368(cB,hfh) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
((1 - hfh) * T) + (hfh * cB) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),((1 - hfh) * T),(hfh * cB)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362(((1 - hfh) * T),(hfh * cB)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
(((1 - hfh) * T) + (hfh * cB)) - T is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K246((TOP-REAL n),(((1 - hfh) * T) + (hfh * cB)),(- T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),(((1 - hfh) * T) + (hfh * cB)),(- T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362((((1 - hfh) * T) + (hfh * cB)),(- T)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K366((((1 - hfh) * T) + (hfh * cB)),T) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
hfh * (cB - T) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368((cB - T),hfh) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
x is Relation-like Function-like V137() V138() V139() Element of the carrier of (Euclid n)
dist (x,A) is V21() real ext-real non negative Element of REAL
|.(hfh * (cB - T)).| is V21() real ext-real non negative Element of REAL
abs hfh is V21() real ext-real Element of REAL
(abs hfh) * |.(cB - T).| is V21() real ext-real Element of REAL
hfh * (dist (FR,A)) is V21() real ext-real Element of REAL
(hfh * (dist (FR,A))) / (dist (FR,A)) is V21() real ext-real Element of REAL
(dist (FR,A)) " is V21() real ext-real non negative set
(hfh * (dist (FR,A))) * ((dist (FR,A)) ") is V21() real ext-real set
(dist (FR,A)) / (dist (FR,A)) is V21() real ext-real non negative Element of REAL
(dist (FR,A)) * ((dist (FR,A)) ") is V21() real ext-real non negative set
hfh * ((dist (FR,A)) / (dist (FR,A))) is V21() real ext-real Element of REAL
hfh * 1 is V21() real ext-real Element of REAL
((diameter F) + 1) / (dist (FR,A)) is V21() real ext-real Element of REAL
((diameter F) + 1) * ((dist (FR,A)) ") is V21() real ext-real set
((diameter F) + 1) / (dist (A,FR)) is V21() real ext-real Element of REAL
(dist (A,FR)) " is V21() real ext-real non negative set
((diameter F) + 1) * ((dist (A,FR)) ") is V21() real ext-real set
sup h is ext-real set
H is V21() real ext-real Element of REAL
1 - H is V21() real ext-real Element of REAL
- H is V21() real ext-real set
1 + (- H) is V21() real ext-real set
(1 - H) * T is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368(T,(1 - H)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
H * cB is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368(cB,H) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
((1 - H) * T) + (H * cB) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),((1 - H) * T),(H * cB)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362(((1 - H) * T),(H * cB)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
x is Relation-like Function-like V137() V138() V139() Element of the carrier of (Euclid n)
hx is V21() real ext-real set
hx / |.(cB - T).| is V21() real ext-real Element of REAL
|.(cB - T).| " is V21() real ext-real non negative set
hx * (|.(cB - T).| ") is V21() real ext-real set
TS is ext-real set
I is V21() real ext-real Element of REAL
1 - I is V21() real ext-real Element of REAL
- I is V21() real ext-real set
1 + (- I) is V21() real ext-real set
(1 - I) * T is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368(T,(1 - I)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
I * cB is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368(cB,I) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
((1 - I) * T) + (I * cB) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),((1 - I) * T),(I * cB)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362(((1 - I) * T),(I * cB)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
H - I is V21() real ext-real Element of REAL
H + (- I) is V21() real ext-real set
abs (H - I) is V21() real ext-real Element of REAL
nN0 is Relation-like Function-like V137() V138() V139() Element of the carrier of (Euclid n)
I * (cB - T) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368((cB - T),I) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
T + (I * (cB - T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),T,(I * (cB - T))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362(T,(I * (cB - T))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
(((1 - H) * T) + (H * cB)) - (T + (I * (cB - T))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
- (T + (I * (cB - T))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K364((T + (I * (cB - T)))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K246((TOP-REAL n),(((1 - H) * T) + (H * cB)),(- (T + (I * (cB - T))))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),(((1 - H) * T) + (H * cB)),(- (T + (I * (cB - T))))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362((((1 - H) * T) + (H * cB)),(- (T + (I * (cB - T))))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K366((((1 - H) * T) + (H * cB)),(T + (I * (cB - T)))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
(((1 - H) * T) + (H * cB)) - T is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K246((TOP-REAL n),(((1 - H) * T) + (H * cB)),(- T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),(((1 - H) * T) + (H * cB)),(- T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362((((1 - H) * T) + (H * cB)),(- T)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K366((((1 - H) * T) + (H * cB)),T) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
((((1 - H) * T) + (H * cB)) - T) - (I * (cB - T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
- (I * (cB - T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K364((I * (cB - T))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K246((TOP-REAL n),((((1 - H) * T) + (H * cB)) - T),(- (I * (cB - T)))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),((((1 - H) * T) + (H * cB)) - T),(- (I * (cB - T)))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362(((((1 - H) * T) + (H * cB)) - T),(- (I * (cB - T)))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K366(((((1 - H) * T) + (H * cB)) - T),(I * (cB - T))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
H * (cB - T) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368((cB - T),H) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
(H * (cB - T)) - (I * (cB - T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K246((TOP-REAL n),(H * (cB - T)),(- (I * (cB - T)))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),(H * (cB - T)),(- (I * (cB - T)))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362((H * (cB - T)),(- (I * (cB - T)))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K366((H * (cB - T)),(I * (cB - T))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
(H - I) * (cB - T) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368((cB - T),(H - I)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
dist (x,nN0) is V21() real ext-real non negative Element of REAL
|.((H - I) * (cB - T)).| is V21() real ext-real non negative Element of REAL
(H - I) * |.(cB - T).| is V21() real ext-real Element of REAL
H - (hx / |.(cB - T).|) is V21() real ext-real Element of REAL
- (hx / |.(cB - T).|) is V21() real ext-real set
H + (- (hx / |.(cB - T).|)) is V21() real ext-real set
H - {} is V21() real ext-real Element of REAL
H + (- {}) is V21() real ext-real set
the topology of (TOP-REAL n) is non empty open Element of K19(K19( the carrier of (TOP-REAL n)))
K19(K19( the carrier of (TOP-REAL n))) is non empty set
TopStruct(# the carrier of (TOP-REAL n), the topology of (TOP-REAL n) #) is non empty strict TopSpace-like TopStruct
TopSpaceMetr (Euclid n) is non empty strict TopSpace-like TopStruct
the carrier of (TopSpaceMetr (Euclid n)) is non empty set
K19( the carrier of (TopSpaceMetr (Euclid n))) is non empty set
hx is functional complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
FrA is Element of K19( the carrier of (TopSpaceMetr (Euclid n)))
the topology of (TopSpaceMetr (Euclid n)) is non empty open Element of K19(K19( the carrier of (TopSpaceMetr (Euclid n))))
K19(K19( the carrier of (TopSpaceMetr (Euclid n)))) is non empty set
TS is V21() real ext-real set
Ball (x,TS) is functional complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (Euclid n))
TS / |.(cB - T).| is V21() real ext-real Element of REAL
|.(cB - T).| " is V21() real ext-real non negative set
TS * (|.(cB - T).| ") is V21() real ext-real set
(TS / |.(cB - T).|) / 2 is V21() real ext-real Element of REAL
(TS / |.(cB - T).|) * (2 ") is V21() real ext-real set
H + ((TS / |.(cB - T).|) / 2) is V21() real ext-real Element of REAL
b is Relation-like Function-like V137() V138() V139() Element of the carrier of (Euclid n)
dist (x,b) is V21() real ext-real non negative Element of REAL
(TS / |.(cB - T).|) * |.(cB - T).| is V21() real ext-real Element of REAL
|.(cB - T).| / |.(cB - T).| is V21() real ext-real non negative Element of REAL
|.(cB - T).| * (|.(cB - T).| ") is V21() real ext-real non negative set
TS * (|.(cB - T).| / |.(cB - T).|) is V21() real ext-real Element of REAL
TS * 1 is V21() real ext-real Element of REAL
H + {} is V21() real ext-real Element of REAL
H - (H + ((TS / |.(cB - T).|) / 2)) is V21() real ext-real Element of REAL
- (H + ((TS / |.(cB - T).|) / 2)) is V21() real ext-real set
H + (- (H + ((TS / |.(cB - T).|) / 2))) is V21() real ext-real set
abs (H - (H + ((TS / |.(cB - T).|) / 2))) is V21() real ext-real Element of REAL
- (H - (H + ((TS / |.(cB - T).|) / 2))) is V21() real ext-real Element of REAL
1 - (H + ((TS / |.(cB - T).|) / 2)) is V21() real ext-real Element of REAL
1 + (- (H + ((TS / |.(cB - T).|) / 2))) is V21() real ext-real set
(1 - (H + ((TS / |.(cB - T).|) / 2))) * T is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368(T,(1 - (H + ((TS / |.(cB - T).|) / 2)))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
(H + ((TS / |.(cB - T).|) / 2)) * cB is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368(cB,(H + ((TS / |.(cB - T).|) / 2))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
((1 - (H + ((TS / |.(cB - T).|) / 2))) * T) + ((H + ((TS / |.(cB - T).|) / 2)) * cB) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),((1 - (H + ((TS / |.(cB - T).|) / 2))) * T),((H + ((TS / |.(cB - T).|) / 2)) * cB)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362(((1 - (H + ((TS / |.(cB - T).|) / 2))) * T),((H + ((TS / |.(cB - T).|) / 2)) * cB)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
FRA is Relation-like Function-like V137() V138() V139() Element of the carrier of (Euclid n)
(((1 - H) * T) + (H * cB)) - (((1 - (H + ((TS / |.(cB - T).|) / 2))) * T) + ((H + ((TS / |.(cB - T).|) / 2)) * cB)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
- (((1 - (H + ((TS / |.(cB - T).|) / 2))) * T) + ((H + ((TS / |.(cB - T).|) / 2)) * cB)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K364((((1 - (H + ((TS / |.(cB - T).|) / 2))) * T) + ((H + ((TS / |.(cB - T).|) / 2)) * cB))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K246((TOP-REAL n),(((1 - H) * T) + (H * cB)),(- (((1 - (H + ((TS / |.(cB - T).|) / 2))) * T) + ((H + ((TS / |.(cB - T).|) / 2)) * cB)))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),(((1 - H) * T) + (H * cB)),(- (((1 - (H + ((TS / |.(cB - T).|) / 2))) * T) + ((H + ((TS / |.(cB - T).|) / 2)) * cB)))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362((((1 - H) * T) + (H * cB)),(- (((1 - (H + ((TS / |.(cB - T).|) / 2))) * T) + ((H + ((TS / |.(cB - T).|) / 2)) * cB)))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K366((((1 - H) * T) + (H * cB)),(((1 - (H + ((TS / |.(cB - T).|) / 2))) * T) + ((H + ((TS / |.(cB - T).|) / 2)) * cB))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
(H + ((TS / |.(cB - T).|) / 2)) * (cB - T) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368((cB - T),(H + ((TS / |.(cB - T).|) / 2))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
T + ((H + ((TS / |.(cB - T).|) / 2)) * (cB - T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),T,((H + ((TS / |.(cB - T).|) / 2)) * (cB - T))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362(T,((H + ((TS / |.(cB - T).|) / 2)) * (cB - T))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
(((1 - H) * T) + (H * cB)) - (T + ((H + ((TS / |.(cB - T).|) / 2)) * (cB - T))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
- (T + ((H + ((TS / |.(cB - T).|) / 2)) * (cB - T))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K364((T + ((H + ((TS / |.(cB - T).|) / 2)) * (cB - T)))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K246((TOP-REAL n),(((1 - H) * T) + (H * cB)),(- (T + ((H + ((TS / |.(cB - T).|) / 2)) * (cB - T))))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),(((1 - H) * T) + (H * cB)),(- (T + ((H + ((TS / |.(cB - T).|) / 2)) * (cB - T))))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362((((1 - H) * T) + (H * cB)),(- (T + ((H + ((TS / |.(cB - T).|) / 2)) * (cB - T))))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K366((((1 - H) * T) + (H * cB)),(T + ((H + ((TS / |.(cB - T).|) / 2)) * (cB - T)))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
(((1 - H) * T) + (H * cB)) - T is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K246((TOP-REAL n),(((1 - H) * T) + (H * cB)),(- T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),(((1 - H) * T) + (H * cB)),(- T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362((((1 - H) * T) + (H * cB)),(- T)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K366((((1 - H) * T) + (H * cB)),T) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
((((1 - H) * T) + (H * cB)) - T) - ((H + ((TS / |.(cB - T).|) / 2)) * (cB - T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
- ((H + ((TS / |.(cB - T).|) / 2)) * (cB - T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K364(((H + ((TS / |.(cB - T).|) / 2)) * (cB - T))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K246((TOP-REAL n),((((1 - H) * T) + (H * cB)) - T),(- ((H + ((TS / |.(cB - T).|) / 2)) * (cB - T)))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),((((1 - H) * T) + (H * cB)) - T),(- ((H + ((TS / |.(cB - T).|) / 2)) * (cB - T)))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362(((((1 - H) * T) + (H * cB)) - T),(- ((H + ((TS / |.(cB - T).|) / 2)) * (cB - T)))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K366(((((1 - H) * T) + (H * cB)) - T),((H + ((TS / |.(cB - T).|) / 2)) * (cB - T))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
H * (cB - T) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368((cB - T),H) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
(H * (cB - T)) - ((H + ((TS / |.(cB - T).|) / 2)) * (cB - T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K246((TOP-REAL n),(H * (cB - T)),(- ((H + ((TS / |.(cB - T).|) / 2)) * (cB - T)))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),(H * (cB - T)),(- ((H + ((TS / |.(cB - T).|) / 2)) * (cB - T)))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362((H * (cB - T)),(- ((H + ((TS / |.(cB - T).|) / 2)) * (cB - T)))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K366((H * (cB - T)),((H + ((TS / |.(cB - T).|) / 2)) * (cB - T))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
(H - (H + ((TS / |.(cB - T).|) / 2))) * (cB - T) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368((cB - T),(H - (H + ((TS / |.(cB - T).|) / 2)))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
dist (x,FRA) is V21() real ext-real non negative Element of REAL
|.((H - (H + ((TS / |.(cB - T).|) / 2))) * (cB - T)).| is V21() real ext-real non negative Element of REAL
((TS / |.(cB - T).|) / 2) * |.(cB - T).| is V21() real ext-real Element of REAL
TS / 2 is V21() real ext-real Element of REAL
TS * (2 ") is V21() real ext-real set
hx \ s is functional complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
abs H is V21() real ext-real Element of REAL
FrA is Relation-like Function-like V137() V138() V139() Element of the carrier of (Euclid n)
hx is Relation-like Function-like V137() V138() V139() Element of the carrier of (Euclid n)
dist (FrA,x) is V21() real ext-real non negative Element of REAL
|.(H * (cB - T)).| is V21() real ext-real non negative Element of REAL
H * |.(cB - T).| is V21() real ext-real Element of REAL
TS is V21() real ext-real set
1 - TS is V21() real ext-real Element of REAL
- TS is V21() real ext-real set
1 + (- TS) is V21() real ext-real set
(1 - TS) * T is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368(T,(1 - TS)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
TS * cB is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368(cB,TS) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
((1 - TS) * T) + (TS * cB) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),((1 - TS) * T),(TS * cB)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362(((1 - TS) * T),(TS * cB)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
abs TS is V21() real ext-real Element of REAL
dist (FrA,hx) is V21() real ext-real non negative Element of REAL
(((1 - TS) * T) + (TS * cB)) - T is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K246((TOP-REAL n),(((1 - TS) * T) + (TS * cB)),(- T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),(((1 - TS) * T) + (TS * cB)),(- T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362((((1 - TS) * T) + (TS * cB)),(- T)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K366((((1 - TS) * T) + (TS * cB)),T) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
TS * (cB - T) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368((cB - T),TS) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
|.(TS * (cB - T)).| is V21() real ext-real non negative Element of REAL
TS * |.(cB - T).| is V21() real ext-real Element of REAL
hx is V21() real ext-real set
n is V21() ordinal natural real V32() cardinal ext-real non negative set
TOP-REAL n is non empty V90() V91() V160() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V188() TopSpace-like T_0 T_1 T_2 strict add-continuous Mult-continuous V310() V311() finite-dimensional RLTopStruct
the carrier of (TOP-REAL n) is functional non empty complex-functions-membered ext-real-functions-membered real-functions-membered set
K19( the carrier of (TOP-REAL n)) is non empty set
T is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
cB is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
halfline (T,cB) is functional closed complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
{ (((1 - b₁) * T) + (b₁ * cB)) where b₁ is V21() real ext-real Element of REAL : 0 <= b₁ } is set
Euclid n is non empty strict Reflexive discerning V65() triangle V310() V311() MetrStruct
A is functional complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
A /\ (halfline (T,cB)) is functional complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
Fr A is functional closed complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
(Fr A) /\ (halfline (T,cB)) is functional closed complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
the carrier of (Euclid n) is functional non empty complex-functions-membered ext-real-functions-membered real-functions-membered set
FR is Relation-like Function-like V137() V138() V139() Element of the carrier of (Euclid n)
Ts is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
T - Ts is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
- Ts is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K364(Ts) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K246((TOP-REAL n),T,(- Ts)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
the U6 of (TOP-REAL n) is Relation-like K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)) -defined the carrier of (TOP-REAL n) -valued Function-like non empty V14(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n))) quasi_total Function-yielding V275() complex-functions-valued ext-real-functions-valued real-functions-valued Element of K19(K20(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)), the carrier of (TOP-REAL n)))
K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)) is Relation-like non empty set
K20(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)), the carrier of (TOP-REAL n)) is Relation-like non empty set
K19(K20(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)), the carrier of (TOP-REAL n))) is non empty set
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),T,(- Ts)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362(T,(- Ts)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K366(T,Ts) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
|.(T - Ts).| is V21() real ext-real non negative Element of REAL
f is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
F is Relation-like Function-like V137() V138() V139() Element of the carrier of (Euclid n)
N is Relation-like Function-like V137() V138() V139() Element of the carrier of (Euclid n)
dist (F,N) is V21() real ext-real non negative Element of REAL
T - f is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
- f is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K364(f) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K246((TOP-REAL n),T,(- f)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),T,(- f)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362(T,(- f)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K366(T,f) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
|.(T - f).| is V21() real ext-real non negative Element of REAL
dist (F,FR) is V21() real ext-real non negative Element of REAL
f is V21() real ext-real set
N is Relation-like Function-like V137() V138() V139() Element of the carrier of (Euclid n)
dist (FR,N) is V21() real ext-real non negative Element of REAL
TN is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
Ts - TN is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
- TN is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K364(TN) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K246((TOP-REAL n),Ts,(- TN)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),Ts,(- TN)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362(Ts,(- TN)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K366(Ts,TN) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
|.(Ts - TN).| is V21() real ext-real non negative Element of REAL
n is V21() ordinal natural real V32() cardinal ext-real non negative set
TOP-REAL n is non empty V90() V91() V160() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V188() TopSpace-like T_0 T_1 T_2 strict add-continuous Mult-continuous V310() V311() finite-dimensional RLTopStruct
the carrier of (TOP-REAL n) is functional non empty complex-functions-membered ext-real-functions-membered real-functions-membered set
K19( the carrier of (TOP-REAL n)) is non empty set
T is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
cB is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
halfline (T,cB) is functional closed complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
{ (((1 - b₁) * T) + (b₁ * cB)) where b₁ is V21() real ext-real Element of REAL : 0 <= b₁ } is set
Euclid n is non empty strict Reflexive discerning V65() triangle V310() V311() MetrStruct
A is functional convex complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
Int A is functional convex open complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
A /\ (halfline (T,cB)) is functional complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
Fr A is functional closed complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
(Fr A) /\ (halfline (T,cB)) is functional closed complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
the carrier of (Euclid n) is functional non empty complex-functions-membered ext-real-functions-membered real-functions-membered set
the topology of (TOP-REAL n) is non empty open Element of K19(K19( the carrier of (TOP-REAL n)))
K19(K19( the carrier of (TOP-REAL n))) is non empty set
TopStruct(# the carrier of (TOP-REAL n), the topology of (TOP-REAL n) #) is non empty strict TopSpace-like TopStruct
TopSpaceMetr (Euclid n) is non empty strict TopSpace-like TopStruct
the carrier of (TopSpaceMetr (Euclid n)) is non empty set
K19( the carrier of (TopSpaceMetr (Euclid n))) is non empty set
the topology of (TopSpaceMetr (Euclid n)) is non empty open Element of K19(K19( the carrier of (TopSpaceMetr (Euclid n))))
K19(K19( the carrier of (TopSpaceMetr (Euclid n)))) is non empty set
F is Element of K19( the carrier of (TopSpaceMetr (Euclid n)))
FR is Relation-like Function-like V137() V138() V139() Element of the carrier of (Euclid n)
f is V21() real ext-real set
Ball (FR,f) is functional complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (Euclid n))
K19( the carrier of (Euclid n)) is non empty set
dist (FR,FR) is V21() real ext-real non negative Element of REAL
TN is functional bounded complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (Euclid n))
h is Relation-like Function-like V137() V138() V139() Element of the carrier of (Euclid n)
hfh is V21() real ext-real set
1 - hfh is V21() real ext-real Element of REAL
- hfh is V21() real ext-real set
1 + (- hfh) is V21() real ext-real set
(1 - hfh) * T is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368(T,(1 - hfh)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
hfh * cB is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368(cB,hfh) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
((1 - hfh) * T) + (hfh * cB) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
the U6 of (TOP-REAL n) is Relation-like K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)) -defined the carrier of (TOP-REAL n) -valued Function-like non empty V14(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n))) quasi_total Function-yielding V275() complex-functions-valued ext-real-functions-valued real-functions-valued Element of K19(K20(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)), the carrier of (TOP-REAL n)))
K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)) is Relation-like non empty set
K20(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)), the carrier of (TOP-REAL n)) is Relation-like non empty set
K19(K20(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)), the carrier of (TOP-REAL n))) is non empty set
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),((1 - hfh) * T),(hfh * cB)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362(((1 - hfh) * T),(hfh * cB)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
{h} is functional non empty V12() V32() 1 -element bounded complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (Euclid n))
x is set
hx is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
FrA is V21() real ext-real set
1 - FrA is V21() real ext-real Element of REAL
- FrA is V21() real ext-real set
1 + (- FrA) is V21() real ext-real set
(1 - FrA) * T is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368(T,(1 - FrA)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
FrA * cB is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368(cB,FrA) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
((1 - FrA) * T) + (FrA * cB) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),((1 - FrA) * T),(FrA * cB)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362(((1 - FrA) * T),(FrA * cB)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
abs FrA is V21() real ext-real Element of REAL
hfh - FrA is V21() real ext-real set
hfh + (- FrA) is V21() real ext-real set
(((1 - FrA) * T) + (FrA * cB)) - T is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
- T is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K364(T) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K246((TOP-REAL n),(((1 - FrA) * T) + (FrA * cB)),(- T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),(((1 - FrA) * T) + (FrA * cB)),(- T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362((((1 - FrA) * T) + (FrA * cB)),(- T)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K366((((1 - FrA) * T) + (FrA * cB)),T) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
cB - T is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K246((TOP-REAL n),cB,(- T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),cB,(- T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362(cB,(- T)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K366(cB,T) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
FrA * (cB - T) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368((cB - T),FrA) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
TS is Relation-like Function-like V137() V138() V139() Element of the carrier of (Euclid n)
dist (TS,FR) is V21() real ext-real non negative Element of REAL
|.(FrA * (cB - T)).| is V21() real ext-real non negative Element of REAL
|.(cB - T).| is V21() real ext-real non negative Element of REAL
FrA * |.(cB - T).| is V21() real ext-real Element of REAL
f * (hfh - FrA) is V21() real ext-real set
(f * (hfh - FrA)) / hfh is V21() real ext-real Element of COMPLEX
hfh " is V21() real ext-real set
(f * (hfh - FrA)) * (hfh ") is V21() real ext-real set
Ball (TS,((f * (hfh - FrA)) / hfh)) is functional complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (Euclid n))
(hfh - FrA) / hfh is V21() real ext-real Element of COMPLEX
(hfh - FrA) * (hfh ") is V21() real ext-real set
nN0 is Element of K19( the carrier of (TopSpaceMetr (Euclid n)))
abs hfh is V21() real ext-real Element of REAL
(((1 - hfh) * T) + (hfh * cB)) - T is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K246((TOP-REAL n),(((1 - hfh) * T) + (hfh * cB)),(- T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),(((1 - hfh) * T) + (hfh * cB)),(- T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362((((1 - hfh) * T) + (hfh * cB)),(- T)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K366((((1 - hfh) * T) + (hfh * cB)),T) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
hfh * (cB - T) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368((cB - T),hfh) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
dist (h,FR) is V21() real ext-real non negative Element of REAL
|.(hfh * (cB - T)).| is V21() real ext-real non negative Element of REAL
hfh * |.(cB - T).| is V21() real ext-real Element of REAL
1 - ((hfh - FrA) / hfh) is V21() real ext-real Element of REAL
- ((hfh - FrA) / hfh) is V21() real ext-real set
1 + (- ((hfh - FrA) / hfh)) is V21() real ext-real set
hfh / hfh is V21() real ext-real Element of COMPLEX
hfh * (hfh ") is V21() real ext-real set
(hfh / hfh) - ((hfh - FrA) / hfh) is V21() real ext-real Element of COMPLEX
(hfh / hfh) + (- ((hfh - FrA) / hfh)) is V21() real ext-real set
FrA / hfh is V21() real ext-real Element of COMPLEX
FrA * (hfh ") is V21() real ext-real set
((hfh - FrA) / hfh) - ((hfh - FrA) / hfh) is V21() real ext-real Element of COMPLEX
((hfh - FrA) / hfh) + (- ((hfh - FrA) / hfh)) is V21() real ext-real set
(hfh * (cB - T)) + T is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),(hfh * (cB - T)),T) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362((hfh * (cB - T)),T) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
T + (FrA * (cB - T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),T,(FrA * (cB - T))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362(T,(FrA * (cB - T))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
(((1 - hfh) * T) + (hfh * cB)) - (((1 - FrA) * T) + (FrA * cB)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
- (((1 - FrA) * T) + (FrA * cB)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K364((((1 - FrA) * T) + (FrA * cB))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K246((TOP-REAL n),(((1 - hfh) * T) + (hfh * cB)),(- (((1 - FrA) * T) + (FrA * cB)))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),(((1 - hfh) * T) + (hfh * cB)),(- (((1 - FrA) * T) + (FrA * cB)))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362((((1 - hfh) * T) + (hfh * cB)),(- (((1 - FrA) * T) + (FrA * cB)))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K366((((1 - hfh) * T) + (hfh * cB)),(((1 - FrA) * T) + (FrA * cB))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
T + (hfh * (cB - T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),T,(hfh * (cB - T))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362(T,(hfh * (cB - T))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
(T + (hfh * (cB - T))) - T is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K246((TOP-REAL n),(T + (hfh * (cB - T))),(- T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),(T + (hfh * (cB - T))),(- T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362((T + (hfh * (cB - T))),(- T)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K366((T + (hfh * (cB - T))),T) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
((T + (hfh * (cB - T))) - T) - (FrA * (cB - T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
- (FrA * (cB - T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K364((FrA * (cB - T))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K246((TOP-REAL n),((T + (hfh * (cB - T))) - T),(- (FrA * (cB - T)))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),((T + (hfh * (cB - T))) - T),(- (FrA * (cB - T)))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362(((T + (hfh * (cB - T))) - T),(- (FrA * (cB - T)))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K366(((T + (hfh * (cB - T))) - T),(FrA * (cB - T))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
T - T is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K246((TOP-REAL n),T,(- T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),T,(- T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362(T,(- T)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K366(T,T) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
(hfh * (cB - T)) + (T - T) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),(hfh * (cB - T)),(T - T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362((hfh * (cB - T)),(T - T)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
((hfh * (cB - T)) + (T - T)) - (FrA * (cB - T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K246((TOP-REAL n),((hfh * (cB - T)) + (T - T)),(- (FrA * (cB - T)))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),((hfh * (cB - T)) + (T - T)),(- (FrA * (cB - T)))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362(((hfh * (cB - T)) + (T - T)),(- (FrA * (cB - T)))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K366(((hfh * (cB - T)) + (T - T)),(FrA * (cB - T))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
0. (TOP-REAL n) is Relation-like Function-like n -element V48( TOP-REAL n) V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
the ZeroF of (TOP-REAL n) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
(hfh * (cB - T)) + (0. (TOP-REAL n)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),(hfh * (cB - T)),(0. (TOP-REAL n))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362((hfh * (cB - T)),(0. (TOP-REAL n))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
((hfh * (cB - T)) + (0. (TOP-REAL n))) - (FrA * (cB - T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K246((TOP-REAL n),((hfh * (cB - T)) + (0. (TOP-REAL n))),(- (FrA * (cB - T)))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),((hfh * (cB - T)) + (0. (TOP-REAL n))),(- (FrA * (cB - T)))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362(((hfh * (cB - T)) + (0. (TOP-REAL n))),(- (FrA * (cB - T)))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K366(((hfh * (cB - T)) + (0. (TOP-REAL n))),(FrA * (cB - T))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
(hfh * (cB - T)) - (FrA * (cB - T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K246((TOP-REAL n),(hfh * (cB - T)),(- (FrA * (cB - T)))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),(hfh * (cB - T)),(- (FrA * (cB - T)))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362((hfh * (cB - T)),(- (FrA * (cB - T)))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K366((hfh * (cB - T)),(FrA * (cB - T))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
(hfh - FrA) * (cB - T) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368((cB - T),(hfh - FrA)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
dist (TS,h) is V21() real ext-real non negative Element of REAL
|.((hfh - FrA) * (cB - T)).| is V21() real ext-real non negative Element of REAL
abs (hfh - FrA) is V21() real ext-real Element of REAL
(abs (hfh - FrA)) * |.(cB - T).| is V21() real ext-real Element of REAL
dist (TS,TS) is V21() real ext-real non negative Element of REAL
B is functional open complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
B \ A is functional complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
FRA is set
H is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
H - hx is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
- hx is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K364(hx) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K246((TOP-REAL n),H,(- hx)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),H,(- hx)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362(H,(- hx)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K366(H,hx) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
hfh / (hfh - FrA) is V21() real ext-real Element of COMPLEX
(hfh - FrA) " is V21() real ext-real set
hfh * ((hfh - FrA) ") is V21() real ext-real set
(hfh / (hfh - FrA)) * (H - hx) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368((H - hx),(hfh / (hfh - FrA))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
T + ((hfh / (hfh - FrA)) * (H - hx)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),T,((hfh / (hfh - FrA)) * (H - hx))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362(T,((hfh / (hfh - FrA)) * (H - hx))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
HH is Relation-like Function-like V137() V138() V139() Element of the carrier of (Euclid n)
dist (TS,HH) is V21() real ext-real non negative Element of REAL
hx - H is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
- H is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K364(H) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K246((TOP-REAL n),hx,(- H)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),hx,(- H)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362(hx,(- H)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K366(hx,H) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
|.(hx - H).| is V21() real ext-real non negative Element of REAL
(hfh / (hfh - FrA)) * ((f * (hfh - FrA)) / hfh) is V21() real ext-real Element of COMPLEX
(hfh / hfh) * (hfh - FrA) is V21() real ext-real set
((hfh / hfh) * (hfh - FrA)) / (hfh - FrA) is V21() real ext-real Element of COMPLEX
((hfh / hfh) * (hfh - FrA)) * ((hfh - FrA) ") is V21() real ext-real set
(((hfh / hfh) * (hfh - FrA)) / (hfh - FrA)) * f is V21() real ext-real set
(hfh - FrA) / (hfh - FrA) is V21() real ext-real Element of COMPLEX
(hfh - FrA) * ((hfh - FrA) ") is V21() real ext-real set
((hfh - FrA) / (hfh - FrA)) * f is V21() real ext-real set
abs (- hfh) is V21() real ext-real Element of REAL
- (- hfh) is V21() real ext-real set
(- hfh) / (hfh - FrA) is V21() real ext-real Element of COMPLEX
(- hfh) * ((hfh - FrA) ") is V21() real ext-real set
abs ((- hfh) / (hfh - FrA)) is V21() real ext-real Element of REAL
(FrA / hfh) * (hfh * (cB - T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368((hfh * (cB - T)),(FrA / hfh)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
(FrA / hfh) * hfh is V21() real ext-real set
((FrA / hfh) * hfh) * (cB - T) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368((cB - T),((FrA / hfh) * hfh)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
(hfh / hfh) * FrA is V21() real ext-real set
((hfh / hfh) * FrA) * (cB - T) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368((cB - T),((hfh / hfh) * FrA)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
T - (T + ((hfh / (hfh - FrA)) * (H - hx))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
- (T + ((hfh / (hfh - FrA)) * (H - hx))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K364((T + ((hfh / (hfh - FrA)) * (H - hx)))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K246((TOP-REAL n),T,(- (T + ((hfh / (hfh - FrA)) * (H - hx))))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),T,(- (T + ((hfh / (hfh - FrA)) * (H - hx))))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362(T,(- (T + ((hfh / (hfh - FrA)) * (H - hx))))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K366(T,(T + ((hfh / (hfh - FrA)) * (H - hx)))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
(T - T) - ((hfh / (hfh - FrA)) * (H - hx)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
- ((hfh / (hfh - FrA)) * (H - hx)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K364(((hfh / (hfh - FrA)) * (H - hx))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K246((TOP-REAL n),(T - T),(- ((hfh / (hfh - FrA)) * (H - hx)))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),(T - T),(- ((hfh / (hfh - FrA)) * (H - hx)))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362((T - T),(- ((hfh / (hfh - FrA)) * (H - hx)))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K366((T - T),((hfh / (hfh - FrA)) * (H - hx))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
(0. (TOP-REAL n)) - ((hfh / (hfh - FrA)) * (H - hx)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K246((TOP-REAL n),(0. (TOP-REAL n)),(- ((hfh / (hfh - FrA)) * (H - hx)))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),(0. (TOP-REAL n)),(- ((hfh / (hfh - FrA)) * (H - hx)))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362((0. (TOP-REAL n)),(- ((hfh / (hfh - FrA)) * (H - hx)))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K366((0. (TOP-REAL n)),((hfh / (hfh - FrA)) * (H - hx))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
(- 1) * ((hfh / (hfh - FrA)) * (H - hx)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368(((hfh / (hfh - FrA)) * (H - hx)),(- 1)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
(- 1) * (hfh / (hfh - FrA)) is V21() real ext-real Element of REAL
((- 1) * (hfh / (hfh - FrA))) * (H - hx) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368((H - hx),((- 1) * (hfh / (hfh - FrA)))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
((- hfh) / (hfh - FrA)) * (H - hx) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368((H - hx),((- hfh) / (hfh - FrA))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
H1 is Relation-like Function-like V137() V138() V139() Element of the carrier of (Euclid n)
dist (FR,H1) is V21() real ext-real non negative Element of REAL
|.(((- hfh) / (hfh - FrA)) * (H - hx)).| is V21() real ext-real non negative Element of REAL
|.(H - hx).| is V21() real ext-real non negative Element of REAL
(hfh / (hfh - FrA)) * |.(H - hx).| is V21() real ext-real Element of REAL
(hfh / (hfh - FrA)) * |.(hx - H).| is V21() real ext-real Element of REAL
((hfh - FrA) / hfh) * ((hfh / (hfh - FrA)) * (H - hx)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368(((hfh / (hfh - FrA)) * (H - hx)),((hfh - FrA) / hfh)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
((hfh - FrA) / hfh) * (hfh / (hfh - FrA)) is V21() real ext-real Element of COMPLEX
(((hfh - FrA) / hfh) * (hfh / (hfh - FrA))) * (H - hx) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368((H - hx),(((hfh - FrA) / hfh) * (hfh / (hfh - FrA)))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
((hfh - FrA) / (hfh - FrA)) * hfh is V21() real ext-real set
(((hfh - FrA) / (hfh - FrA)) * hfh) / hfh is V21() real ext-real Element of COMPLEX
(((hfh - FrA) / (hfh - FrA)) * hfh) * (hfh ") is V21() real ext-real set
((((hfh - FrA) / (hfh - FrA)) * hfh) / hfh) * (H - hx) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368((H - hx),((((hfh - FrA) / (hfh - FrA)) * hfh) / hfh)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
(hfh / hfh) * (H - hx) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368((H - hx),(hfh / hfh)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
1 * (H - hx) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368((H - hx),1) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
((hfh - FrA) / hfh) * (T + ((hfh / (hfh - FrA)) * (H - hx))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368((T + ((hfh / (hfh - FrA)) * (H - hx))),((hfh - FrA) / hfh)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
((hfh - FrA) / hfh) * T is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368(T,((hfh - FrA) / hfh)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
(((hfh - FrA) / hfh) * T) + (H - hx) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),(((hfh - FrA) / hfh) * T),(H - hx)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362((((hfh - FrA) / hfh) * T),(H - hx)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
H is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
(1 - ((hfh - FrA) / hfh)) * H is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368(H,(1 - ((hfh - FrA) / hfh))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
(((hfh - FrA) / hfh) * (T + ((hfh / (hfh - FrA)) * (H - hx)))) + ((1 - ((hfh - FrA) / hfh)) * H) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),(((hfh - FrA) / hfh) * (T + ((hfh / (hfh - FrA)) * (H - hx)))),((1 - ((hfh - FrA) / hfh)) * H)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362((((hfh - FrA) / hfh) * (T + ((hfh / (hfh - FrA)) * (H - hx)))),((1 - ((hfh - FrA) / hfh)) * H)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
(H - hx) + (((hfh - FrA) / hfh) * T) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),(H - hx),(((hfh - FrA) / hfh) * T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362((H - hx),(((hfh - FrA) / hfh) * T)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
(1 - ((hfh - FrA) / hfh)) * T is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368(T,(1 - ((hfh - FrA) / hfh))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
((1 - ((hfh - FrA) / hfh)) * T) + (FrA * (cB - T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),((1 - ((hfh - FrA) / hfh)) * T),(FrA * (cB - T))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362(((1 - ((hfh - FrA) / hfh)) * T),(FrA * (cB - T))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
((H - hx) + (((hfh - FrA) / hfh) * T)) + (((1 - ((hfh - FrA) / hfh)) * T) + (FrA * (cB - T))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),((H - hx) + (((hfh - FrA) / hfh) * T)),(((1 - ((hfh - FrA) / hfh)) * T) + (FrA * (cB - T)))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362(((H - hx) + (((hfh - FrA) / hfh) * T)),(((1 - ((hfh - FrA) / hfh)) * T) + (FrA * (cB - T)))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
((H - hx) + (((hfh - FrA) / hfh) * T)) + ((1 - ((hfh - FrA) / hfh)) * T) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),((H - hx) + (((hfh - FrA) / hfh) * T)),((1 - ((hfh - FrA) / hfh)) * T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362(((H - hx) + (((hfh - FrA) / hfh) * T)),((1 - ((hfh - FrA) / hfh)) * T)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
(((H - hx) + (((hfh - FrA) / hfh) * T)) + ((1 - ((hfh - FrA) / hfh)) * T)) + (FrA * (cB - T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),(((H - hx) + (((hfh - FrA) / hfh) * T)) + ((1 - ((hfh - FrA) / hfh)) * T)),(FrA * (cB - T))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362((((H - hx) + (((hfh - FrA) / hfh) * T)) + ((1 - ((hfh - FrA) / hfh)) * T)),(FrA * (cB - T))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
(((hfh - FrA) / hfh) * T) + ((1 - ((hfh - FrA) / hfh)) * T) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),(((hfh - FrA) / hfh) * T),((1 - ((hfh - FrA) / hfh)) * T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362((((hfh - FrA) / hfh) * T),((1 - ((hfh - FrA) / hfh)) * T)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
(H - hx) + ((((hfh - FrA) / hfh) * T) + ((1 - ((hfh - FrA) / hfh)) * T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),(H - hx),((((hfh - FrA) / hfh) * T) + ((1 - ((hfh - FrA) / hfh)) * T))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362((H - hx),((((hfh - FrA) / hfh) * T) + ((1 - ((hfh - FrA) / hfh)) * T))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
((H - hx) + ((((hfh - FrA) / hfh) * T) + ((1 - ((hfh - FrA) / hfh)) * T))) + (FrA * (cB - T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),((H - hx) + ((((hfh - FrA) / hfh) * T) + ((1 - ((hfh - FrA) / hfh)) * T))),(FrA * (cB - T))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362(((H - hx) + ((((hfh - FrA) / hfh) * T) + ((1 - ((hfh - FrA) / hfh)) * T))),(FrA * (cB - T))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
((hfh - FrA) / hfh) + (1 - ((hfh - FrA) / hfh)) is V21() real ext-real Element of REAL
(((hfh - FrA) / hfh) + (1 - ((hfh - FrA) / hfh))) * T is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368(T,(((hfh - FrA) / hfh) + (1 - ((hfh - FrA) / hfh)))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
(H - hx) + ((((hfh - FrA) / hfh) + (1 - ((hfh - FrA) / hfh))) * T) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),(H - hx),((((hfh - FrA) / hfh) + (1 - ((hfh - FrA) / hfh))) * T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362((H - hx),((((hfh - FrA) / hfh) + (1 - ((hfh - FrA) / hfh))) * T)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
((H - hx) + ((((hfh - FrA) / hfh) + (1 - ((hfh - FrA) / hfh))) * T)) + (FrA * (cB - T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),((H - hx) + ((((hfh - FrA) / hfh) + (1 - ((hfh - FrA) / hfh))) * T)),(FrA * (cB - T))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362(((H - hx) + ((((hfh - FrA) / hfh) + (1 - ((hfh - FrA) / hfh))) * T)),(FrA * (cB - T))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
(H - hx) + T is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),(H - hx),T) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362((H - hx),T) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
((H - hx) + T) + (FrA * (cB - T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),((H - hx) + T),(FrA * (cB - T))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362(((H - hx) + T),(FrA * (cB - T))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
(H - hx) + hx is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),(H - hx),hx) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362((H - hx),hx) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
hx - hx is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K246((TOP-REAL n),hx,(- hx)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),hx,(- hx)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362(hx,(- hx)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K366(hx,hx) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
H - (hx - hx) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
- (hx - hx) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K364((hx - hx)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K246((TOP-REAL n),H,(- (hx - hx))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),H,(- (hx - hx))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362(H,(- (hx - hx))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K366(H,(hx - hx)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
H - (0. (TOP-REAL n)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
- (0. (TOP-REAL n)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K364((0. (TOP-REAL n))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K246((TOP-REAL n),H,(- (0. (TOP-REAL n)))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),H,(- (0. (TOP-REAL n)))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362(H,(- (0. (TOP-REAL n)))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K366(H,(0. (TOP-REAL n))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
n is V21() ordinal natural real V30() V31() V32() cardinal ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered Element of NAT
TOP-REAL n is non empty V90() V91() V160() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V188() TopSpace-like T_0 T_1 T_2 strict add-continuous Mult-continuous V310() V311() finite-dimensional RLTopStruct
the carrier of (TOP-REAL n) is functional non empty complex-functions-membered ext-real-functions-membered real-functions-membered set
K19( the carrier of (TOP-REAL n)) is non empty set
0* n is Relation-like NAT -defined REAL -valued Function-like n -element V76() V137() V138() V139() Element of REAL n
REAL n is functional non empty V78() complex-functions-membered ext-real-functions-membered real-functions-membered M10( REAL )
0. (TOP-REAL n) is Relation-like Function-like n -element V48( TOP-REAL n) V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
the ZeroF of (TOP-REAL n) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
Tdisk ((0. (TOP-REAL n)),1) is non empty TopSpace-like T_0 T_1 T_2 V307(n) V310() V311() SubSpace of TOP-REAL n
cl_Ball ((0. (TOP-REAL n)),1) is functional non empty convex closed bounded compact complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
{ b₁ where b₁ is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n) : |.(b₁ - (0. (TOP-REAL n))).| <= 1 } is set
(TOP-REAL n) | (cl_Ball ((0. (TOP-REAL n)),1)) is non empty strict TopSpace-like T_0 T_1 T_2 compact V310() V311() SubSpace of TOP-REAL n
the carrier of (Tdisk ((0. (TOP-REAL n)),1)) is functional non empty complex-functions-membered ext-real-functions-membered real-functions-membered set
Sphere ((0. (TOP-REAL n)),1) is functional closed bounded compact complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
{ b₁ where b₁ is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n) : |.(b₁ - (0. (TOP-REAL n))).| = 1 } is set
Euclid n is non empty strict Reflexive discerning V65() triangle V310() V311() MetrStruct
{(0. (TOP-REAL n))} is functional non empty V12() V32() 1 -element closed bounded compact complex-functions-membered ext-real-functions-membered real-functions-membered affinely-independent Element of K19( the carrier of (TOP-REAL n))
the carrier of (TOP-REAL n) \ {(0. (TOP-REAL n))} is functional complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
{(0. (TOP-REAL n))} ` is functional open complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
s is functional non empty open complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
(TOP-REAL n) | s is non empty strict TopSpace-like T_0 T_1 T_2 V310() V311() SubSpace of TOP-REAL n
n NormF is Relation-like the carrier of (TOP-REAL n) -defined the carrier of R^1 -valued Function-like non empty V14( the carrier of (TOP-REAL n)) quasi_total V137() V138() V139() continuous Element of K19(K20( the carrier of (TOP-REAL n), the carrier of R^1))
K20( the carrier of (TOP-REAL n), the carrier of R^1) is Relation-like non empty V137() V138() V139() set
K19(K20( the carrier of (TOP-REAL n), the carrier of R^1)) is non empty set
(0. (TOP-REAL n)) .--> (0. (TOP-REAL n)) is Relation-like the carrier of (TOP-REAL n) -defined {(0. (TOP-REAL n))} -defined the carrier of (TOP-REAL n) -valued Function-like one-to-one V32() Function-yielding V275() complex-functions-valued set
{(0. (TOP-REAL n))} is functional non empty V12() V32() 1 -element complex-functions-membered set
TN is functional convex complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
Int TN is functional convex open complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
(TOP-REAL n) | TN is strict TopSpace-like T_0 T_1 T_2 V310() V311() SubSpace of TOP-REAL n
the carrier of ((TOP-REAL n) | TN) is functional complex-functions-membered ext-real-functions-membered real-functions-membered set
K20( the carrier of ((TOP-REAL n) | TN), the carrier of (Tdisk ((0. (TOP-REAL n)),1))) is Relation-like set
K19(K20( the carrier of ((TOP-REAL n) | TN), the carrier of (Tdisk ((0. (TOP-REAL n)),1)))) is non empty set
Fr TN is functional closed complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
the carrier of (Euclid n) is functional non empty complex-functions-membered ext-real-functions-membered real-functions-membered set
h is Relation-like Function-like V137() V138() V139() Element of the carrier of (Euclid n)
H is V21() real ext-real set
Ball (h,H) is functional complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (Euclid n))
K19( the carrier of (Euclid n)) is non empty set
(Fr TN) \ {(0. (TOP-REAL n))} is functional complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
TopSpaceMetr (Euclid n) is non empty strict TopSpace-like TopStruct
[#] ((TOP-REAL n) | s) is functional non empty non proper open closed dense non boundary complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of ((TOP-REAL n) | s))
the carrier of ((TOP-REAL n) | s) is functional non empty complex-functions-membered ext-real-functions-membered real-functions-membered set
K19( the carrier of ((TOP-REAL n) | s)) is non empty set
the topology of (TOP-REAL n) is non empty open Element of K19(K19( the carrier of (TOP-REAL n)))
K19(K19( the carrier of (TOP-REAL n))) is non empty set
TopStruct(# the carrier of (TOP-REAL n), the topology of (TOP-REAL n) #) is non empty strict TopSpace-like TopStruct
the carrier of (TopSpaceMetr (Euclid n)) is non empty set
K19( the carrier of (TopSpaceMetr (Euclid n))) is non empty set
x is Element of K19( the carrier of (TopSpaceMetr (Euclid n)))
(TopSpaceMetr (Euclid n)) | x is strict TopSpace-like SubSpace of TopSpaceMetr (Euclid n)
FrA is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
halfline ((0. (TOP-REAL n)),FrA) is functional non empty convex closed complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
{ (((1 - b₁) * (0. (TOP-REAL n))) + (b₁ * FrA)) where b₁ is V21() real ext-real Element of REAL : 0 <= b₁ } is set
(Fr TN) /\ (halfline ((0. (TOP-REAL n)),FrA)) is functional closed complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
TN /\ (halfline ((0. (TOP-REAL n)),FrA)) is functional convex complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
hx is functional complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (Euclid n))
TS is functional complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (Euclid n))
the Relation-like Function-like V137() V138() V139() Element of s is Relation-like Function-like V137() V138() V139() Element of s
halfline ((0. (TOP-REAL n)), the Relation-like Function-like V137() V138() V139() Element of s) is functional non empty convex closed complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
{ (((1 - b₁) * (0. (TOP-REAL n))) + (b₁ * the Relation-like Function-like V137() V138() V139() Element of s)) where b₁ is V21() real ext-real Element of REAL : 0 <= b₁ } is set
(Fr TN) /\ (halfline ((0. (TOP-REAL n)), the Relation-like Function-like V137() V138() V139() Element of s)) is functional closed complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
TS is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
{TS} is functional non empty V12() V32() 1 -element closed bounded compact complex-functions-membered ext-real-functions-membered real-functions-membered affinely-independent Element of K19( the carrier of (TOP-REAL n))
(TOP-REAL n) | (Sphere ((0. (TOP-REAL n)),1)) is strict TopSpace-like T_0 T_1 T_2 compact V310() V311() SubSpace of TOP-REAL n
K20( the carrier of ((TOP-REAL n) | s), the carrier of (TOP-REAL n)) is Relation-like non empty set
K19(K20( the carrier of ((TOP-REAL n) | s), the carrier of (TOP-REAL n))) is non empty set
incl ((TOP-REAL n) | s) is Relation-like the carrier of ((TOP-REAL n) | s) -defined the carrier of (TOP-REAL n) -valued Function-like non empty V14( the carrier of ((TOP-REAL n) | s)) quasi_total Function-yielding V275() complex-functions-valued ext-real-functions-valued real-functions-valued Element of K19(K20( the carrier of ((TOP-REAL n) | s), the carrier of (TOP-REAL n)))
[#] ((TOP-REAL n) | (Sphere ((0. (TOP-REAL n)),1))) is functional non proper open closed dense complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of ((TOP-REAL n) | (Sphere ((0. (TOP-REAL n)),1))))
the carrier of ((TOP-REAL n) | (Sphere ((0. (TOP-REAL n)),1))) is functional complex-functions-membered ext-real-functions-membered real-functions-membered set
K19( the carrier of ((TOP-REAL n) | (Sphere ((0. (TOP-REAL n)),1)))) is non empty set
(n NormF) | ((TOP-REAL n) | s) is Relation-like the carrier of ((TOP-REAL n) | s) -defined the carrier of R^1 -valued Function-like non empty V14( the carrier of ((TOP-REAL n) | s)) quasi_total V137() V138() V139() continuous Element of K19(K20( the carrier of ((TOP-REAL n) | s), the carrier of R^1))
K20( the carrier of ((TOP-REAL n) | s), the carrier of R^1) is Relation-like non empty V137() V138() V139() set
K19(K20( the carrier of ((TOP-REAL n) | s), the carrier of R^1)) is non empty set
(n NormF) | the carrier of ((TOP-REAL n) | s) is Relation-like the carrier of (TOP-REAL n) -defined the carrier of ((TOP-REAL n) | s) -defined the carrier of (TOP-REAL n) -defined the carrier of R^1 -valued Function-like V137() V138() V139() Element of K19(K20( the carrier of (TOP-REAL n), the carrier of R^1))
rng ((n NormF) | ((TOP-REAL n) | s)) is non empty complex-membered ext-real-membered real-membered Element of K19( the carrier of R^1)
K19( the carrier of R^1) is non empty set
dom ((n NormF) | ((TOP-REAL n) | s)) is functional non empty complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of ((TOP-REAL n) | s))
nN0 is set
((n NormF) | ((TOP-REAL n) | s)) . nN0 is V21() real ext-real set
dom (n NormF) is functional non empty complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
b is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
(n NormF) . b is V21() real ext-real Element of the carrier of R^1
B is Relation-like NAT -defined REAL -valued Function-like n -element V76() V137() V138() V139() Element of REAL n
|.B.| is V21() real ext-real non negative Element of REAL
I is Relation-like the carrier of ((TOP-REAL n) | s) -defined the carrier of (TOP-REAL n) -valued Function-like non empty V14( the carrier of ((TOP-REAL n) | s)) quasi_total continuous Function-yielding V275() complex-functions-valued ext-real-functions-valued real-functions-valued Element of K19(K20( the carrier of ((TOP-REAL n) | s), the carrier of (TOP-REAL n)))
nN0 is Relation-like non-empty the carrier of ((TOP-REAL n) | s) -defined the carrier of R^1 -valued Function-like non empty V14( the carrier of ((TOP-REAL n) | s)) quasi_total V137() V138() V139() continuous Element of K19(K20( the carrier of ((TOP-REAL n) | s), the carrier of R^1))
I </> nN0 is Relation-like the carrier of ((TOP-REAL n) | s) /\ (dom nN0) -defined R_PFuncs (DOMS the carrier of (TOP-REAL n)) -valued Function-like Function-yielding V275() complex-functions-valued ext-real-functions-valued real-functions-valued Element of K19(K20(( the carrier of ((TOP-REAL n) | s) /\ (dom nN0)),(R_PFuncs (DOMS the carrier of (TOP-REAL n)))))
dom nN0 is non empty set
the carrier of ((TOP-REAL n) | s) /\ (dom nN0) is set
DOMS the carrier of (TOP-REAL n) is set
R_PFuncs (DOMS the carrier of (TOP-REAL n)) is functional complex-functions-membered ext-real-functions-membered real-functions-membered set
K20(( the carrier of ((TOP-REAL n) | s) /\ (dom nN0)),(R_PFuncs (DOMS the carrier of (TOP-REAL n)))) is Relation-like set
K19(K20(( the carrier of ((TOP-REAL n) | s) /\ (dom nN0)),(R_PFuncs (DOMS the carrier of (TOP-REAL n))))) is non empty set
b is Relation-like the carrier of ((TOP-REAL n) | s) -defined the carrier of (TOP-REAL n) -valued Function-like non empty V14( the carrier of ((TOP-REAL n) | s)) quasi_total Function-yielding V275() complex-functions-valued ext-real-functions-valued real-functions-valued Element of K19(K20( the carrier of ((TOP-REAL n) | s), the carrier of (TOP-REAL n)))
dom b is functional non empty complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of ((TOP-REAL n) | s))
B is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
b . B is Relation-like Function-like V137() V138() V139() set
|.B.| is V21() real ext-real non negative Element of REAL
1 / |.B.| is V21() real ext-real non negative Element of REAL
|.B.| " is V21() real ext-real non negative set
1 * (|.B.| ") is V21() real ext-real non negative set
(1 / |.B.|) * B is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368(B,(1 / |.B.|)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
|.((1 / |.B.|) * B).| is V21() real ext-real non negative Element of REAL
nN0 . B is V21() real ext-real set
(n NormF) . B is V21() real ext-real Element of the carrier of R^1
I . B is Relation-like Function-like V137() V138() V139() set
(I . B) (/) (nN0 . B) is Relation-like Function-like V137() V138() V139() set
B (/) |.B.| is Relation-like Function-like V76() V137() V138() V139() set
(1 / |.B.|) (#) B is Relation-like Function-like set
abs (1 / |.B.|) is V21() real ext-real Element of REAL
(abs (1 / |.B.|)) * |.B.| is V21() real ext-real Element of REAL
rng b is functional non empty complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
B is set
FRA is set
b . FRA is Relation-like Function-like V137() V138() V139() set
H is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
|.H.| is V21() real ext-real non negative Element of REAL
1 / |.H.| is V21() real ext-real non negative Element of REAL
|.H.| " is V21() real ext-real non negative set
1 * (|.H.| ") is V21() real ext-real non negative set
(1 / |.H.|) * H is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368(H,(1 / |.H.|)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
((1 / |.H.|) * H) - (0. (TOP-REAL n)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
- (0. (TOP-REAL n)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K364((0. (TOP-REAL n))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K246((TOP-REAL n),((1 / |.H.|) * H),(- (0. (TOP-REAL n)))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
the U6 of (TOP-REAL n) is Relation-like K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)) -defined the carrier of (TOP-REAL n) -valued Function-like non empty V14(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n))) quasi_total Function-yielding V275() complex-functions-valued ext-real-functions-valued real-functions-valued Element of K19(K20(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)), the carrier of (TOP-REAL n)))
K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)) is Relation-like non empty set
K20(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)), the carrier of (TOP-REAL n)) is Relation-like non empty set
K19(K20(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)), the carrier of (TOP-REAL n))) is non empty set
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),((1 / |.H.|) * H),(- (0. (TOP-REAL n)))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362(((1 / |.H.|) * H),(- (0. (TOP-REAL n)))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K366(((1 / |.H.|) * H),(0. (TOP-REAL n))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
|.((1 / |.H.|) * H).| is V21() real ext-real non negative Element of REAL
K20( the carrier of ((TOP-REAL n) | s), the carrier of ((TOP-REAL n) | (Sphere ((0. (TOP-REAL n)),1)))) is Relation-like set
K19(K20( the carrier of ((TOP-REAL n) | s), the carrier of ((TOP-REAL n) | (Sphere ((0. (TOP-REAL n)),1))))) is non empty set
{(0. (TOP-REAL n))} --> (0. (TOP-REAL n)) is Relation-like {(0. (TOP-REAL n))} -defined the carrier of (TOP-REAL n) -valued Function-like constant non empty V14({(0. (TOP-REAL n))}) quasi_total V32() Function-yielding V275() complex-functions-valued ext-real-functions-valued real-functions-valued Element of K19(K20({(0. (TOP-REAL n))}, the carrier of (TOP-REAL n)))
K20({(0. (TOP-REAL n))}, the carrier of (TOP-REAL n)) is Relation-like non empty set
K19(K20({(0. (TOP-REAL n))}, the carrier of (TOP-REAL n))) is non empty set
dom ((0. (TOP-REAL n)) .--> (0. (TOP-REAL n))) is functional V12() V32() complex-functions-membered Element of K19({(0. (TOP-REAL n))})
K19({(0. (TOP-REAL n))}) is non empty V32() V36() set
FrA is functional non empty complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of ((TOP-REAL n) | s))
((TOP-REAL n) | s) | FrA is non empty strict TopSpace-like T_0 T_1 T_2 V310() V311() SubSpace of (TOP-REAL n) | s
b | (((TOP-REAL n) | s) | FrA) is Relation-like the carrier of (((TOP-REAL n) | s) | FrA) -defined the carrier of (TOP-REAL n) -valued Function-like non empty V14( the carrier of (((TOP-REAL n) | s) | FrA)) quasi_total Function-yielding V275() complex-functions-valued ext-real-functions-valued real-functions-valued Element of K19(K20( the carrier of (((TOP-REAL n) | s) | FrA), the carrier of (TOP-REAL n)))
the carrier of (((TOP-REAL n) | s) | FrA) is functional non empty complex-functions-membered ext-real-functions-membered real-functions-membered set
K20( the carrier of (((TOP-REAL n) | s) | FrA), the carrier of (TOP-REAL n)) is Relation-like non empty set
K19(K20( the carrier of (((TOP-REAL n) | s) | FrA), the carrier of (TOP-REAL n))) is non empty set
dom (b | (((TOP-REAL n) | s) | FrA)) is functional non empty complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (((TOP-REAL n) | s) | FrA))
K19( the carrier of (((TOP-REAL n) | s) | FrA)) is non empty set
b | the carrier of (((TOP-REAL n) | s) | FrA) is Relation-like the carrier of ((TOP-REAL n) | s) -defined the carrier of (((TOP-REAL n) | s) | FrA) -defined the carrier of ((TOP-REAL n) | s) -defined the carrier of (TOP-REAL n) -valued Function-like Function-yielding V275() complex-functions-valued ext-real-functions-valued real-functions-valued Element of K19(K20( the carrier of ((TOP-REAL n) | s), the carrier of (TOP-REAL n)))
rng (b | (((TOP-REAL n) | s) | FrA)) is functional non empty complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
K20( the carrier of (((TOP-REAL n) | s) | FrA), the carrier of ((TOP-REAL n) | (Sphere ((0. (TOP-REAL n)),1)))) is Relation-like set
K19(K20( the carrier of (((TOP-REAL n) | s) | FrA), the carrier of ((TOP-REAL n) | (Sphere ((0. (TOP-REAL n)),1))))) is non empty set
[#] (((TOP-REAL n) | s) | FrA) is functional non empty non proper open closed dense non boundary complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (((TOP-REAL n) | s) | FrA))
H is Relation-like the carrier of (((TOP-REAL n) | s) | FrA) -defined the carrier of ((TOP-REAL n) | (Sphere ((0. (TOP-REAL n)),1))) -valued Function-like quasi_total Function-yielding V275() complex-functions-valued ext-real-functions-valued real-functions-valued Element of K19(K20( the carrier of (((TOP-REAL n) | s) | FrA), the carrier of ((TOP-REAL n) | (Sphere ((0. (TOP-REAL n)),1)))))
rng H is functional complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of ((TOP-REAL n) | (Sphere ((0. (TOP-REAL n)),1))))
H1 is set
HH is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
HH - (0. (TOP-REAL n)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
- (0. (TOP-REAL n)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K364((0. (TOP-REAL n))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K246((TOP-REAL n),HH,(- (0. (TOP-REAL n)))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
the U6 of (TOP-REAL n) is Relation-like K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)) -defined the carrier of (TOP-REAL n) -valued Function-like non empty V14(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n))) quasi_total Function-yielding V275() complex-functions-valued ext-real-functions-valued real-functions-valued Element of K19(K20(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)), the carrier of (TOP-REAL n)))
K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)) is Relation-like non empty set
K20(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)), the carrier of (TOP-REAL n)) is Relation-like non empty set
K19(K20(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)), the carrier of (TOP-REAL n))) is non empty set
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),HH,(- (0. (TOP-REAL n)))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362(HH,(- (0. (TOP-REAL n)))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K366(HH,(0. (TOP-REAL n))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
|.(HH - (0. (TOP-REAL n))).| is V21() real ext-real non negative Element of REAL
halfline ((0. (TOP-REAL n)),HH) is functional non empty convex closed complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
{ (((1 - b₁) * (0. (TOP-REAL n))) + (b₁ * HH)) where b₁ is V21() real ext-real Element of REAL : 0 <= b₁ } is set
FrA /\ (halfline ((0. (TOP-REAL n)),HH)) is functional complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
nN0F is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
{nN0F} is functional non empty V12() V32() 1 -element closed bounded compact complex-functions-membered ext-real-functions-membered real-functions-membered affinely-independent Element of K19( the carrier of (TOP-REAL n))
b . nN0F is Relation-like Function-like V137() V138() V139() set
|.nN0F.| is V21() real ext-real non negative Element of REAL
1 / |.nN0F.| is V21() real ext-real non negative Element of REAL
|.nN0F.| " is V21() real ext-real non negative set
1 * (|.nN0F.| ") is V21() real ext-real non negative set
(1 / |.nN0F.|) * nN0F is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368(nN0F,(1 / |.nN0F.|)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
H . nN0F is Relation-like Function-like V137() V138() V139() set
halfline ((0. (TOP-REAL n)),nN0F) is functional non empty convex closed complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
{ (((1 - b₁) * (0. (TOP-REAL n))) + (b₁ * nN0F)) where b₁ is V21() real ext-real Element of REAL : 0 <= b₁ } is set
((1 / |.nN0F.|) * nN0F) - (0. (TOP-REAL n)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K246((TOP-REAL n),((1 / |.nN0F.|) * nN0F),(- (0. (TOP-REAL n)))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),((1 / |.nN0F.|) * nN0F),(- (0. (TOP-REAL n)))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362(((1 / |.nN0F.|) * nN0F),(- (0. (TOP-REAL n)))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K366(((1 / |.nN0F.|) * nN0F),(0. (TOP-REAL n))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
|.((1 / |.nN0F.|) * nN0F).| is V21() real ext-real non negative Element of REAL
dom H is functional complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (((TOP-REAL n) | s) | FrA))
(TOP-REAL n) | (Fr TN) is strict TopSpace-like T_0 T_1 T_2 V310() V311() SubSpace of TOP-REAL n
H1 is set
HH is set
H . H1 is Relation-like Function-like V137() V138() V139() set
H . HH is Relation-like Function-like V137() V138() V139() set
nN0F is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
b . nN0F is Relation-like Function-like V137() V138() V139() set
|.nN0F.| is V21() real ext-real non negative Element of REAL
1 / |.nN0F.| is V21() real ext-real non negative Element of REAL
|.nN0F.| " is V21() real ext-real non negative set
1 * (|.nN0F.| ") is V21() real ext-real non negative set
(1 / |.nN0F.|) * nN0F is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368(nN0F,(1 / |.nN0F.|)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
H1B is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
halfline ((0. (TOP-REAL n)),H1B) is functional non empty convex closed complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
{ (((1 - b₁) * (0. (TOP-REAL n))) + (b₁ * H1B)) where b₁ is V21() real ext-real Element of REAL : 0 <= b₁ } is set
(Fr TN) /\ (halfline ((0. (TOP-REAL n)),H1B)) is functional closed complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
NH1B is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
{NH1B} is functional non empty V12() V32() 1 -element closed bounded compact complex-functions-membered ext-real-functions-membered real-functions-membered affinely-independent Element of K19( the carrier of (TOP-REAL n))
|.H1B.| is V21() real ext-real non negative Element of REAL
1 / |.H1B.| is V21() real ext-real non negative Element of REAL
|.H1B.| " is V21() real ext-real non negative set
1 * (|.H1B.| ") is V21() real ext-real non negative set
(1 / |.H1B.|) * H1B is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368(H1B,(1 / |.H1B.|)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
|.((1 / |.H1B.|) * H1B).| is V21() real ext-real non negative Element of REAL
(0. (TOP-REAL n)) + ((1 / |.H1B.|) * H1B) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
the U6 of (TOP-REAL n) is Relation-like K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)) -defined the carrier of (TOP-REAL n) -valued Function-like non empty V14(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n))) quasi_total Function-yielding V275() complex-functions-valued ext-real-functions-valued real-functions-valued Element of K19(K20(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)), the carrier of (TOP-REAL n)))
K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)) is Relation-like non empty set
K20(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)), the carrier of (TOP-REAL n)) is Relation-like non empty set
K19(K20(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)), the carrier of (TOP-REAL n))) is non empty set
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),(0. (TOP-REAL n)),((1 / |.H1B.|) * H1B)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362((0. (TOP-REAL n)),((1 / |.H1B.|) * H1B)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
b . H1B is Relation-like Function-like V137() V138() V139() set
b . H1 is Relation-like Function-like V137() V138() V139() set
b . HH is Relation-like Function-like V137() V138() V139() set
1 - (1 / |.nN0F.|) is V21() real ext-real Element of REAL
- (1 / |.nN0F.|) is V21() real ext-real non positive set
1 + (- (1 / |.nN0F.|)) is V21() real ext-real set
(1 - (1 / |.nN0F.|)) * (0. (TOP-REAL n)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368((0. (TOP-REAL n)),(1 - (1 / |.nN0F.|))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
halfline ((0. (TOP-REAL n)),nN0F) is functional non empty convex closed complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
{ (((1 - b₁) * (0. (TOP-REAL n))) + (b₁ * nN0F)) where b₁ is V21() real ext-real Element of REAL : 0 <= b₁ } is set
1 - (1 / |.H1B.|) is V21() real ext-real Element of REAL
- (1 / |.H1B.|) is V21() real ext-real non positive set
1 + (- (1 / |.H1B.|)) is V21() real ext-real set
(1 - (1 / |.H1B.|)) * (0. (TOP-REAL n)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368((0. (TOP-REAL n)),(1 - (1 / |.H1B.|))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
halfline ((0. (TOP-REAL n)),((1 / |.nN0F.|) * nN0F)) is functional non empty convex closed complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
{ (((1 - b₁) * (0. (TOP-REAL n))) + (b₁ * ((1 / |.nN0F.|) * nN0F))) where b₁ is V21() real ext-real Element of REAL : 0 <= b₁ } is set
K20( the carrier of ((TOP-REAL n) | (Sphere ((0. (TOP-REAL n)),1))), the carrier of (((TOP-REAL n) | s) | FrA)) is Relation-like set
K19(K20( the carrier of ((TOP-REAL n) | (Sphere ((0. (TOP-REAL n)),1))), the carrier of (((TOP-REAL n) | s) | FrA))) is non empty set
H /" is Relation-like the carrier of ((TOP-REAL n) | (Sphere ((0. (TOP-REAL n)),1))) -defined the carrier of (((TOP-REAL n) | s) | FrA) -valued Function-like V14( the carrier of ((TOP-REAL n) | (Sphere ((0. (TOP-REAL n)),1)))) quasi_total Function-yielding V275() complex-functions-valued ext-real-functions-valued real-functions-valued Element of K19(K20( the carrier of ((TOP-REAL n) | (Sphere ((0. (TOP-REAL n)),1))), the carrier of (((TOP-REAL n) | s) | FrA)))
nN0 | (((TOP-REAL n) | s) | FrA) is Relation-like the carrier of (((TOP-REAL n) | s) | FrA) -defined the carrier of R^1 -valued Function-like non empty V14( the carrier of (((TOP-REAL n) | s) | FrA)) quasi_total V137() V138() V139() continuous Element of K19(K20( the carrier of (((TOP-REAL n) | s) | FrA), the carrier of R^1))
K20( the carrier of (((TOP-REAL n) | s) | FrA), the carrier of R^1) is Relation-like non empty V137() V138() V139() set
K19(K20( the carrier of (((TOP-REAL n) | s) | FrA), the carrier of R^1)) is non empty set
K20( the carrier of ((TOP-REAL n) | s), the carrier of (((TOP-REAL n) | s) | FrA)) is Relation-like non empty set
K19(K20( the carrier of ((TOP-REAL n) | s), the carrier of (((TOP-REAL n) | s) | FrA))) is non empty set
B is Relation-like the carrier of ((TOP-REAL n) | s) -defined the carrier of ((TOP-REAL n) | (Sphere ((0. (TOP-REAL n)),1))) -valued Function-like quasi_total Function-yielding V275() complex-functions-valued ext-real-functions-valued real-functions-valued Element of K19(K20( the carrier of ((TOP-REAL n) | s), the carrier of ((TOP-REAL n) | (Sphere ((0. (TOP-REAL n)),1)))))
H1 is Relation-like the carrier of ((TOP-REAL n) | (Sphere ((0. (TOP-REAL n)),1))) -defined the carrier of (((TOP-REAL n) | s) | FrA) -valued Function-like V14( the carrier of ((TOP-REAL n) | (Sphere ((0. (TOP-REAL n)),1)))) quasi_total continuous Function-yielding V275() complex-functions-valued ext-real-functions-valued real-functions-valued Element of K19(K20( the carrier of ((TOP-REAL n) | (Sphere ((0. (TOP-REAL n)),1))), the carrier of (((TOP-REAL n) | s) | FrA)))
H1 * B is Relation-like the carrier of ((TOP-REAL n) | s) -defined the carrier of (((TOP-REAL n) | s) | FrA) -valued Function-like Function-yielding V275() complex-functions-valued ext-real-functions-valued real-functions-valued Element of K19(K20( the carrier of ((TOP-REAL n) | s), the carrier of (((TOP-REAL n) | s) | FrA)))
H1B is Relation-like the carrier of ((TOP-REAL n) | s) -defined the carrier of (((TOP-REAL n) | s) | FrA) -valued Function-like non empty V14( the carrier of ((TOP-REAL n) | s)) quasi_total Function-yielding V275() complex-functions-valued ext-real-functions-valued real-functions-valued Element of K19(K20( the carrier of ((TOP-REAL n) | s), the carrier of (((TOP-REAL n) | s) | FrA)))
(nN0 | (((TOP-REAL n) | s) | FrA)) * H1B is Relation-like the carrier of ((TOP-REAL n) | s) -defined the carrier of R^1 -valued Function-like non empty V14( the carrier of ((TOP-REAL n) | s)) quasi_total V137() V138() V139() Element of K19(K20( the carrier of ((TOP-REAL n) | s), the carrier of R^1))
nN0 | the carrier of (((TOP-REAL n) | s) | FrA) is Relation-like the carrier of ((TOP-REAL n) | s) -defined the carrier of (((TOP-REAL n) | s) | FrA) -defined the carrier of ((TOP-REAL n) | s) -defined the carrier of R^1 -valued Function-like V137() V138() V139() Element of K19(K20( the carrier of ((TOP-REAL n) | s), the carrier of R^1))
NH1B is Relation-like the carrier of ((TOP-REAL n) | s) -defined the carrier of R^1 -valued Function-like non empty V14( the carrier of ((TOP-REAL n) | s)) quasi_total V137() V138() V139() Element of K19(K20( the carrier of ((TOP-REAL n) | s), the carrier of R^1))
rng NH1B is non empty complex-membered ext-real-membered real-membered Element of K19( the carrier of R^1)
rng (nN0 | (((TOP-REAL n) | s) | FrA)) is non empty complex-membered ext-real-membered real-membered Element of K19( the carrier of R^1)
rng nN0 is non empty complex-membered ext-real-membered real-membered V209() Element of K19( the carrier of R^1)
NH1B is Relation-like non-empty the carrier of ((TOP-REAL n) | s) -defined the carrier of R^1 -valued Function-like non empty V14( the carrier of ((TOP-REAL n) | s)) quasi_total V137() V138() V139() continuous Element of K19(K20( the carrier of ((TOP-REAL n) | s), the carrier of R^1))
I </> NH1B is Relation-like the carrier of ((TOP-REAL n) | s) /\ (dom NH1B) -defined R_PFuncs (DOMS the carrier of (TOP-REAL n)) -valued Function-like Function-yielding V275() complex-functions-valued ext-real-functions-valued real-functions-valued Element of K19(K20(( the carrier of ((TOP-REAL n) | s) /\ (dom NH1B)),(R_PFuncs (DOMS the carrier of (TOP-REAL n)))))
dom NH1B is non empty set
the carrier of ((TOP-REAL n) | s) /\ (dom NH1B) is set
K20(( the carrier of ((TOP-REAL n) | s) /\ (dom NH1B)),(R_PFuncs (DOMS the carrier of (TOP-REAL n)))) is Relation-like set
K19(K20(( the carrier of ((TOP-REAL n) | s) /\ (dom NH1B)),(R_PFuncs (DOMS the carrier of (TOP-REAL n))))) is non empty set
G is Relation-like the carrier of ((TOP-REAL n) | s) -defined the carrier of (TOP-REAL n) -valued Function-like non empty V14( the carrier of ((TOP-REAL n) | s)) quasi_total Function-yielding V275() complex-functions-valued ext-real-functions-valued real-functions-valued Element of K19(K20( the carrier of ((TOP-REAL n) | s), the carrier of (TOP-REAL n)))
dom G is functional non empty complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of ((TOP-REAL n) | s))
dom (nN0 | (((TOP-REAL n) | s) | FrA)) is functional non empty complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (((TOP-REAL n) | s) | FrA))
G0 is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
H1B . G0 is Relation-like Function-like V137() V138() V139() set
G . G0 is Relation-like Function-like V137() V138() V139() set
dom NH1B is functional non empty complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of ((TOP-REAL n) | s))
G1 is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
(nN0 | (((TOP-REAL n) | s) | FrA)) . G1 is V21() real ext-real set
nN0 . G1 is V21() real ext-real set
(n NormF) . G1 is V21() real ext-real Element of the carrier of R^1
|.G1.| is V21() real ext-real non negative Element of REAL
1 / |.G1.| is V21() real ext-real non negative Element of REAL
|.G1.| " is V21() real ext-real non negative set
1 * (|.G1.| ") is V21() real ext-real non negative set
(1 / |.G1.|) * G0 is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368(G0,(1 / |.G1.|)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
NH1B . G0 is V21() real ext-real set
(nN0 | (((TOP-REAL n) | s) | FrA)) . (H1B . G0) is V21() real ext-real set
I . G0 is Relation-like Function-like V137() V138() V139() set
(I . G0) (/) (NH1B . G0) is Relation-like Function-like V137() V138() V139() set
G0 (/) |.G1.| is Relation-like Function-like V76() V137() V138() V139() set
(1 / |.G1.|) (#) G0 is Relation-like Function-like set
rng G is functional non empty complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
G0 is set
G . G0 is Relation-like Function-like V137() V138() V139() set
G1 is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
H1B . G1 is Relation-like Function-like V137() V138() V139() set
G . G1 is Relation-like Function-like V137() V138() V139() set
TRnCL is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
|.TRnCL.| is V21() real ext-real non negative Element of REAL
1 / |.TRnCL.| is V21() real ext-real non negative Element of REAL
|.TRnCL.| " is V21() real ext-real non negative set
1 * (|.TRnCL.| ") is V21() real ext-real non negative set
(1 / |.TRnCL.|) * G1 is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368(G1,(1 / |.TRnCL.|)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
(dom G) \ (dom ((0. (TOP-REAL n)) .--> (0. (TOP-REAL n)))) is functional complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of ((TOP-REAL n) | s))
G0 is set
G1 is set
((0. (TOP-REAL n)) .--> (0. (TOP-REAL n))) . G0 is Relation-like Function-like V137() set
G . G1 is Relation-like Function-like V137() V138() V139() set
HH is Relation-like Function-like set
HH " is Relation-like Function-like set
G0 is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
halfline ((0. (TOP-REAL n)),G0) is functional non empty convex closed complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
{ (((1 - b₁) * (0. (TOP-REAL n))) + (b₁ * G0)) where b₁ is V21() real ext-real Element of REAL : 0 <= b₁ } is set
(Fr TN) /\ (halfline ((0. (TOP-REAL n)),G0)) is functional closed complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
H1B . G0 is Relation-like Function-like V137() V138() V139() set
{(H1B . G0)} is functional non empty V12() V32() 1 -element complex-functions-membered set
dom H1B is functional non empty complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of ((TOP-REAL n) | s))
B . G0 is Relation-like Function-like V137() V138() V139() set
H1 . (B . G0) is Relation-like Function-like V137() V138() V139() set
dom H1 is functional complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of ((TOP-REAL n) | (Sphere ((0. (TOP-REAL n)),1))))
G1 is set
H . G1 is Relation-like Function-like V137() V138() V139() set
TRnCL is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
H . TRnCL is Relation-like Function-like V137() V138() V139() set
b . TRnCL is Relation-like Function-like V137() V138() V139() set
|.TRnCL.| is V21() real ext-real non negative Element of REAL
|.G0.| is V21() real ext-real non negative Element of REAL
|.TRnCL.| / |.G0.| is V21() real ext-real non negative Element of REAL
|.G0.| " is V21() real ext-real non negative set
|.TRnCL.| * (|.G0.| ") is V21() real ext-real non negative set
1 / |.TRnCL.| is V21() real ext-real non negative Element of REAL
|.TRnCL.| " is V21() real ext-real non negative set
1 * (|.TRnCL.| ") is V21() real ext-real non negative set
(1 / |.TRnCL.|) * TRnCL is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368(TRnCL,(1 / |.TRnCL.|)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
|.((1 / |.TRnCL.|) * TRnCL).| is V21() real ext-real non negative Element of REAL
|.TRnCL.| / |.TRnCL.| is V21() real ext-real non negative Element of REAL
|.TRnCL.| * (|.TRnCL.| ") is V21() real ext-real non negative set
|.TRnCL.| * (1 / |.TRnCL.|) is V21() real ext-real non negative Element of REAL
(|.TRnCL.| * (1 / |.TRnCL.|)) * TRnCL is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368(TRnCL,(|.TRnCL.| * (1 / |.TRnCL.|))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
|.TRnCL.| * ((1 / |.TRnCL.|) * TRnCL) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368(((1 / |.TRnCL.|) * TRnCL),|.TRnCL.|) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
1 / |.G0.| is V21() real ext-real non negative Element of REAL
1 * (|.G0.| ") is V21() real ext-real non negative set
(1 / |.G0.|) * G0 is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368(G0,(1 / |.G0.|)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
|.TRnCL.| * ((1 / |.G0.|) * G0) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368(((1 / |.G0.|) * G0),|.TRnCL.|) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
(|.TRnCL.| / |.G0.|) * G0 is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368(G0,(|.TRnCL.| / |.G0.|)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
GA is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
{GA} is functional non empty V12() V32() 1 -element closed bounded compact complex-functions-membered ext-real-functions-membered real-functions-membered affinely-independent Element of K19( the carrier of (TOP-REAL n))
G0 is set
G1 is set
G . G0 is Relation-like Function-like V137() V138() V139() set
G . G1 is Relation-like Function-like V137() V138() V139() set
TRnCL is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
H1B . TRnCL is Relation-like Function-like V137() V138() V139() set
G . TRnCL is Relation-like Function-like V137() V138() V139() set
GA is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
|.GA.| is V21() real ext-real non negative Element of REAL
1 / |.GA.| is V21() real ext-real non negative Element of REAL
|.GA.| " is V21() real ext-real non negative set
1 * (|.GA.| ") is V21() real ext-real non negative set
(1 / |.GA.|) * TRnCL is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368(TRnCL,(1 / |.GA.|)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
halfline ((0. (TOP-REAL n)),TRnCL) is functional non empty convex closed complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
{ (((1 - b₁) * (0. (TOP-REAL n))) + (b₁ * TRnCL)) where b₁ is V21() real ext-real Element of REAL : 0 <= b₁ } is set
FrA /\ (halfline ((0. (TOP-REAL n)),TRnCL)) is functional complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
{GA} is functional non empty V12() V32() 1 -element closed bounded compact complex-functions-membered ext-real-functions-membered real-functions-membered affinely-independent Element of K19( the carrier of (TOP-REAL n))
TRnA is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
H1B . TRnA is Relation-like Function-like V137() V138() V139() set
G . TRnA is Relation-like Function-like V137() V138() V139() set
GA is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
|.GA.| is V21() real ext-real non negative Element of REAL
1 / |.GA.| is V21() real ext-real non negative Element of REAL
|.GA.| " is V21() real ext-real non negative set
1 * (|.GA.| ") is V21() real ext-real non negative set
(1 / |.GA.|) * TRnA is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368(TRnA,(1 / |.GA.|)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
halfline ((0. (TOP-REAL n)),((1 / |.GA.|) * TRnCL)) is functional non empty convex closed complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
{ (((1 - b₁) * (0. (TOP-REAL n))) + (b₁ * ((1 / |.GA.|) * TRnCL))) where b₁ is V21() real ext-real Element of REAL : 0 <= b₁ } is set
halfline ((0. (TOP-REAL n)),TRnA) is functional non empty convex closed complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
{ (((1 - b₁) * (0. (TOP-REAL n))) + (b₁ * TRnA)) where b₁ is V21() real ext-real Element of REAL : 0 <= b₁ } is set
{GA} is functional non empty V12() V32() 1 -element closed bounded compact complex-functions-membered ext-real-functions-membered real-functions-membered affinely-independent Element of K19( the carrier of (TOP-REAL n))
G +* ((0. (TOP-REAL n)) .--> (0. (TOP-REAL n))) is Relation-like Function-like set
dom (G +* ((0. (TOP-REAL n)) .--> (0. (TOP-REAL n)))) is set
(dom G) \/ (dom ((0. (TOP-REAL n)) .--> (0. (TOP-REAL n)))) is non empty set
s \/ {(0. (TOP-REAL n))} is functional non empty complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
G1 is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
TRnCL is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
H1B . G1 is Relation-like Function-like V137() V138() V139() set
|.TRnCL.| is V21() real ext-real non negative Element of REAL
|.TRnCL.| * G1 is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368(G1,|.TRnCL.|) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
G . (|.TRnCL.| * G1) is Relation-like Function-like V137() V138() V139() set
TRnA is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
H1B . TRnA is Relation-like Function-like V137() V138() V139() set
G . TRnA is Relation-like Function-like V137() V138() V139() set
GA is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
|.GA.| is V21() real ext-real non negative Element of REAL
1 / |.GA.| is V21() real ext-real non negative Element of REAL
|.GA.| " is V21() real ext-real non negative set
1 * (|.GA.| ") is V21() real ext-real non negative set
(1 / |.GA.|) * TRnA is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368(TRnA,(1 / |.GA.|)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
|.GA.| * TRnA is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368(TRnA,|.GA.|) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
H1B . (|.GA.| * TRnA) is Relation-like Function-like V137() V138() V139() set
G . (|.GA.| * TRnA) is Relation-like Function-like V137() V138() V139() set
e2 is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
|.e2.| is V21() real ext-real non negative Element of REAL
1 / |.e2.| is V21() real ext-real non negative Element of REAL
|.e2.| " is V21() real ext-real non negative set
1 * (|.e2.| ") is V21() real ext-real non negative set
(1 / |.e2.|) * (|.GA.| * TRnA) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368((|.GA.| * TRnA),(1 / |.e2.|)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
{GA} is functional non empty V12() V32() 1 -element closed bounded compact complex-functions-membered ext-real-functions-membered real-functions-membered affinely-independent Element of K19( the carrier of (TOP-REAL n))
{e2} is functional non empty V12() V32() 1 -element closed bounded compact complex-functions-membered ext-real-functions-membered real-functions-membered affinely-independent Element of K19( the carrier of (TOP-REAL n))
halfline ((0. (TOP-REAL n)),(|.GA.| * TRnA)) is functional non empty convex closed complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
{ (((1 - b₁) * (0. (TOP-REAL n))) + (b₁ * (|.GA.| * TRnA))) where b₁ is V21() real ext-real Element of REAL : 0 <= b₁ } is set
(Fr TN) /\ (halfline ((0. (TOP-REAL n)),(|.GA.| * TRnA))) is functional closed complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
halfline ((0. (TOP-REAL n)),TRnA) is functional non empty convex closed complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
{ (((1 - b₁) * (0. (TOP-REAL n))) + (b₁ * TRnA)) where b₁ is V21() real ext-real Element of REAL : 0 <= b₁ } is set
(Fr TN) /\ (halfline ((0. (TOP-REAL n)),TRnA)) is functional closed complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
(1 / |.GA.|) * (|.GA.| * TRnA) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368((|.GA.| * TRnA),(1 / |.GA.|)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
|.GA.| / |.GA.| is V21() real ext-real non negative Element of REAL
|.GA.| * (|.GA.| ") is V21() real ext-real non negative set
(|.GA.| / |.GA.|) * TRnA is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368(TRnA,(|.GA.| / |.GA.|)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
1 * TRnA is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368(TRnA,1) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
G .: FrA is functional non empty complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
G1 is set
TRnCL is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
|.TRnCL.| is V21() real ext-real non negative Element of REAL
H1B . TRnCL is Relation-like Function-like V137() V138() V139() set
G . TRnCL is Relation-like Function-like V137() V138() V139() set
TRnA is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
|.TRnA.| is V21() real ext-real non negative Element of REAL
1 / |.TRnA.| is V21() real ext-real non negative Element of REAL
|.TRnA.| " is V21() real ext-real non negative set
1 * (|.TRnA.| ") is V21() real ext-real non negative set
(1 / |.TRnA.|) * TRnCL is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368(TRnCL,(1 / |.TRnA.|)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
|.TRnA.| * TRnCL is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368(TRnCL,|.TRnA.|) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
G . (|.TRnA.| * TRnCL) is Relation-like Function-like V137() V138() V139() set
{TRnA} is functional non empty V12() V32() 1 -element closed bounded compact complex-functions-membered ext-real-functions-membered real-functions-membered affinely-independent Element of K19( the carrier of (TOP-REAL n))
halfline ((0. (TOP-REAL n)),TRnCL) is functional non empty convex closed complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
{ (((1 - b₁) * (0. (TOP-REAL n))) + (b₁ * TRnCL)) where b₁ is V21() real ext-real Element of REAL : 0 <= b₁ } is set
(Fr TN) /\ (halfline ((0. (TOP-REAL n)),TRnCL)) is functional closed complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
TRnA - (0. (TOP-REAL n)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
- (0. (TOP-REAL n)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K364((0. (TOP-REAL n))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K246((TOP-REAL n),TRnA,(- (0. (TOP-REAL n)))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
the U6 of (TOP-REAL n) is Relation-like K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)) -defined the carrier of (TOP-REAL n) -valued Function-like non empty V14(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n))) quasi_total Function-yielding V275() complex-functions-valued ext-real-functions-valued real-functions-valued Element of K19(K20(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)), the carrier of (TOP-REAL n)))
K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)) is Relation-like non empty set
K20(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)), the carrier of (TOP-REAL n)) is Relation-like non empty set
K19(K20(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)), the carrier of (TOP-REAL n))) is non empty set
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),TRnA,(- (0. (TOP-REAL n)))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362(TRnA,(- (0. (TOP-REAL n)))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K366(TRnA,(0. (TOP-REAL n))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
abs |.TRnA.| is V21() real ext-real Element of REAL
|.(|.TRnA.| * TRnCL).| is V21() real ext-real non negative Element of REAL
|.TRnA.| * |.TRnCL.| is V21() real ext-real non negative Element of REAL
|.TRnA.| * 1 is V21() real ext-real non negative Element of REAL
(|.TRnA.| * TRnCL) - (0. (TOP-REAL n)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K246((TOP-REAL n),(|.TRnA.| * TRnCL),(- (0. (TOP-REAL n)))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),(|.TRnA.| * TRnCL),(- (0. (TOP-REAL n)))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362((|.TRnA.| * TRnCL),(- (0. (TOP-REAL n)))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K366((|.TRnA.| * TRnCL),(0. (TOP-REAL n))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
((0. (TOP-REAL n)) .--> (0. (TOP-REAL n))) . (0. (TOP-REAL n)) is Relation-like Function-like V137() set
rng ((0. (TOP-REAL n)) .--> (0. (TOP-REAL n))) is functional V32() closed bounded compact complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
rng (G +* ((0. (TOP-REAL n)) .--> (0. (TOP-REAL n)))) is set
(rng G) \/ {(0. (TOP-REAL n))} is functional non empty complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)) is Relation-like non empty set
K19(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n))) is non empty set
G1 is Relation-like the carrier of (TOP-REAL n) -defined the carrier of (TOP-REAL n) -valued Function-like one-to-one non empty V14( the carrier of (TOP-REAL n)) quasi_total Function-yielding V275() complex-functions-valued ext-real-functions-valued real-functions-valued Element of K19(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)))
G1 . (0. (TOP-REAL n)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
TRnCL is set
TRnA is set
G . TRnA is Relation-like Function-like V137() V138() V139() set
GA is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
H1B . GA is Relation-like Function-like V137() V138() V139() set
G . GA is Relation-like Function-like V137() V138() V139() set
GA is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
|.GA.| is V21() real ext-real non negative Element of REAL
1 / |.GA.| is V21() real ext-real non negative Element of REAL
|.GA.| " is V21() real ext-real non negative set
1 * (|.GA.| ") is V21() real ext-real non negative set
(1 / |.GA.|) * GA is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368(GA,(1 / |.GA.|)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
halfline ((0. (TOP-REAL n)),GA) is functional non empty convex closed complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
{ (((1 - b₁) * (0. (TOP-REAL n))) + (b₁ * GA)) where b₁ is V21() real ext-real Element of REAL : 0 <= b₁ } is set
FrA /\ (halfline ((0. (TOP-REAL n)),GA)) is functional complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
{GA} is functional non empty V12() V32() 1 -element closed bounded compact complex-functions-membered ext-real-functions-membered real-functions-membered affinely-independent Element of K19( the carrier of (TOP-REAL n))
abs (1 / |.GA.|) is V21() real ext-real Element of REAL
|.((1 / |.GA.|) * GA).| is V21() real ext-real non negative Element of REAL
(1 / |.GA.|) * |.GA.| is V21() real ext-real non negative Element of REAL
((1 / |.GA.|) * GA) - (0. (TOP-REAL n)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
- (0. (TOP-REAL n)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K364((0. (TOP-REAL n))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K246((TOP-REAL n),((1 / |.GA.|) * GA),(- (0. (TOP-REAL n)))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
the U6 of (TOP-REAL n) is Relation-like K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)) -defined the carrier of (TOP-REAL n) -valued Function-like non empty V14(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n))) quasi_total Function-yielding V275() complex-functions-valued ext-real-functions-valued real-functions-valued Element of K19(K20(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)), the carrier of (TOP-REAL n)))
K20(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)), the carrier of (TOP-REAL n)) is Relation-like non empty set
K19(K20(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)), the carrier of (TOP-REAL n))) is non empty set
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),((1 / |.GA.|) * GA),(- (0. (TOP-REAL n)))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362(((1 / |.GA.|) * GA),(- (0. (TOP-REAL n)))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K366(((1 / |.GA.|) * GA),(0. (TOP-REAL n))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
|.(((1 / |.GA.|) * GA) - (0. (TOP-REAL n))).| is V21() real ext-real non negative Element of REAL
G1 | ((TOP-REAL n) | TN) is Relation-like the carrier of ((TOP-REAL n) | TN) -defined the carrier of (TOP-REAL n) -valued Function-like V14( the carrier of ((TOP-REAL n) | TN)) quasi_total Function-yielding V275() complex-functions-valued ext-real-functions-valued real-functions-valued Element of K19(K20( the carrier of ((TOP-REAL n) | TN), the carrier of (TOP-REAL n)))
K20( the carrier of ((TOP-REAL n) | TN), the carrier of (TOP-REAL n)) is Relation-like set
K19(K20( the carrier of ((TOP-REAL n) | TN), the carrier of (TOP-REAL n))) is non empty set
G1 | the carrier of ((TOP-REAL n) | TN) is Relation-like the carrier of (TOP-REAL n) -defined the carrier of ((TOP-REAL n) | TN) -defined the carrier of (TOP-REAL n) -defined the carrier of (TOP-REAL n) -valued Function-like Function-yielding V275() complex-functions-valued ext-real-functions-valued real-functions-valued Element of K19(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)))
[#] ((TOP-REAL n) | TN) is functional non proper open closed dense complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of ((TOP-REAL n) | TN))
K19( the carrier of ((TOP-REAL n) | TN)) is non empty set
dom (G1 | ((TOP-REAL n) | TN)) is functional complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of ((TOP-REAL n) | TN))
rng (G1 | ((TOP-REAL n) | TN)) is functional complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
GA is set
e2 is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
(G1 | ((TOP-REAL n) | TN)) . (0. (TOP-REAL n)) is Relation-like Function-like V137() V138() V139() set
e2 is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
halfline ((0. (TOP-REAL n)),e2) is functional non empty convex closed complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
{ (((1 - b₁) * (0. (TOP-REAL n))) + (b₁ * e2)) where b₁ is V21() real ext-real Element of REAL : 0 <= b₁ } is set
H1B . e2 is Relation-like Function-like V137() V138() V139() set
G . e2 is Relation-like Function-like V137() V138() V139() set
U is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
|.U.| is V21() real ext-real non negative Element of REAL
1 / |.U.| is V21() real ext-real non negative Element of REAL
|.U.| " is V21() real ext-real non negative set
1 * (|.U.| ") is V21() real ext-real non negative set
(1 / |.U.|) * e2 is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368(e2,(1 / |.U.|)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
abs |.U.| is V21() real ext-real Element of REAL
(Fr TN) /\ (halfline ((0. (TOP-REAL n)),e2)) is functional closed complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
{U} is functional non empty V12() V32() 1 -element closed bounded compact complex-functions-membered ext-real-functions-membered real-functions-membered affinely-independent Element of K19( the carrier of (TOP-REAL n))
halfline ((0. (TOP-REAL n)),U) is functional non empty convex closed complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
{ (((1 - b₁) * (0. (TOP-REAL n))) + (b₁ * U)) where b₁ is V21() real ext-real Element of REAL : 0 <= b₁ } is set
|.e2.| is V21() real ext-real non negative Element of REAL
|.e2.| * U is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368(U,|.e2.|) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
1 - |.e2.| is V21() real ext-real Element of REAL
- |.e2.| is V21() real ext-real non positive set
1 + (- |.e2.|) is V21() real ext-real set
(1 - |.e2.|) * (0. (TOP-REAL n)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368((0. (TOP-REAL n)),(1 - |.e2.|)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
(|.e2.| * U) + ((1 - |.e2.|) * (0. (TOP-REAL n))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
the U6 of (TOP-REAL n) is Relation-like K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)) -defined the carrier of (TOP-REAL n) -valued Function-like non empty V14(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n))) quasi_total Function-yielding V275() complex-functions-valued ext-real-functions-valued real-functions-valued Element of K19(K20(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)), the carrier of (TOP-REAL n)))
K20(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)), the carrier of (TOP-REAL n)) is Relation-like non empty set
K19(K20(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)), the carrier of (TOP-REAL n))) is non empty set
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),(|.e2.| * U),((1 - |.e2.|) * (0. (TOP-REAL n)))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362((|.e2.| * U),((1 - |.e2.|) * (0. (TOP-REAL n)))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
(G1 | ((TOP-REAL n) | TN)) . (|.e2.| * U) is Relation-like Function-like V137() V138() V139() set
G1 . (|.e2.| * U) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
|.U.| * e2 is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368(e2,|.U.|) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
G . (|.U.| * e2) is Relation-like Function-like V137() V138() V139() set
G1 . (|.U.| * e2) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
abs |.e2.| is V21() real ext-real Element of REAL
|.(|.e2.| * U).| is V21() real ext-real non negative Element of REAL
|.e2.| * |.U.| is V21() real ext-real non negative Element of REAL
|.(|.U.| * e2).| is V21() real ext-real non negative Element of REAL
(|.e2.| * U) - (0. (TOP-REAL n)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
- (0. (TOP-REAL n)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K364((0. (TOP-REAL n))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K246((TOP-REAL n),(|.e2.| * U),(- (0. (TOP-REAL n)))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),(|.e2.| * U),(- (0. (TOP-REAL n)))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362((|.e2.| * U),(- (0. (TOP-REAL n)))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K366((|.e2.| * U),(0. (TOP-REAL n))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
|.((|.e2.| * U) - (0. (TOP-REAL n))).| is V21() real ext-real non negative Element of REAL
(|.U.| * e2) - (0. (TOP-REAL n)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K246((TOP-REAL n),(|.U.| * e2),(- (0. (TOP-REAL n)))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),(|.U.| * e2),(- (0. (TOP-REAL n)))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362((|.U.| * e2),(- (0. (TOP-REAL n)))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K366((|.U.| * e2),(0. (TOP-REAL n))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
|.((|.U.| * e2) - (0. (TOP-REAL n))).| is V21() real ext-real non negative Element of REAL
e2 is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
GA is set
e2 is set
(G1 | ((TOP-REAL n) | TN)) . e2 is Relation-like Function-like V137() V138() V139() set
x is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
(G1 | ((TOP-REAL n) | TN)) . x is Relation-like Function-like V137() V138() V139() set
G1 . x is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
(G1 . x) - (0. (TOP-REAL n)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
- (0. (TOP-REAL n)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K364((0. (TOP-REAL n))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K246((TOP-REAL n),(G1 . x),(- (0. (TOP-REAL n)))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
the U6 of (TOP-REAL n) is Relation-like K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)) -defined the carrier of (TOP-REAL n) -valued Function-like non empty V14(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n))) quasi_total Function-yielding V275() complex-functions-valued ext-real-functions-valued real-functions-valued Element of K19(K20(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)), the carrier of (TOP-REAL n)))
K20(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)), the carrier of (TOP-REAL n)) is Relation-like non empty set
K19(K20(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)), the carrier of (TOP-REAL n))) is non empty set
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),(G1 . x),(- (0. (TOP-REAL n)))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362((G1 . x),(- (0. (TOP-REAL n)))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K366((G1 . x),(0. (TOP-REAL n))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
|.((G1 . x) - (0. (TOP-REAL n))).| is V21() real ext-real non negative Element of REAL
halfline ((0. (TOP-REAL n)),x) is functional non empty convex closed complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
{ (((1 - b₁) * (0. (TOP-REAL n))) + (b₁ * x)) where b₁ is V21() real ext-real Element of REAL : 0 <= b₁ } is set
TN /\ (halfline ((0. (TOP-REAL n)),x)) is functional convex complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
hx is functional complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (Euclid n))
0TRn is functional complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (Euclid n))
(Fr TN) /\ (halfline ((0. (TOP-REAL n)),x)) is functional closed complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
r is Relation-like Function-like V137() V138() V139() Element of the carrier of (Euclid n)
H1B . x is Relation-like Function-like V137() V138() V139() set
G . x is Relation-like Function-like V137() V138() V139() set
Bx is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
|.Bx.| is V21() real ext-real non negative Element of REAL
1 / |.Bx.| is V21() real ext-real non negative Element of REAL
|.Bx.| " is V21() real ext-real non negative set
1 * (|.Bx.| ") is V21() real ext-real non negative set
(1 / |.Bx.|) * x is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368(x,(1 / |.Bx.|)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
abs (1 / |.Bx.|) is V21() real ext-real Element of REAL
|.((1 / |.Bx.|) * x).| is V21() real ext-real non negative Element of REAL
|.x.| is V21() real ext-real non negative Element of REAL
|.x.| / |.Bx.| is V21() real ext-real non negative Element of REAL
|.x.| * (|.Bx.| ") is V21() real ext-real non negative set
{Bx} is functional non empty V12() V32() 1 -element closed bounded compact complex-functions-membered ext-real-functions-membered real-functions-membered affinely-independent Element of K19( the carrier of (TOP-REAL n))
dist (h,r) is V21() real ext-real non negative Element of REAL
(0. (TOP-REAL n)) - Bx is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
- Bx is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K364(Bx) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K246((TOP-REAL n),(0. (TOP-REAL n)),(- Bx)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),(0. (TOP-REAL n)),(- Bx)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362((0. (TOP-REAL n)),(- Bx)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K366((0. (TOP-REAL n)),Bx) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
|.((0. (TOP-REAL n)) - Bx).| is V21() real ext-real non negative Element of REAL
|.(- Bx).| is V21() real ext-real non negative Element of REAL
B is Relation-like Function-like V137() V138() V139() Element of the carrier of (Euclid n)
dist (h,B) is V21() real ext-real non negative Element of REAL
(0. (TOP-REAL n)) - x is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
- x is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K364(x) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K246((TOP-REAL n),(0. (TOP-REAL n)),(- x)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),(0. (TOP-REAL n)),(- x)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362((0. (TOP-REAL n)),(- x)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K366((0. (TOP-REAL n)),x) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
|.((0. (TOP-REAL n)) - x).| is V21() real ext-real non negative Element of REAL
|.(- x).| is V21() real ext-real non negative Element of REAL
|.(G1 . x).| is V21() real ext-real non negative Element of REAL
[#] ((TOP-REAL n) | (cl_Ball ((0. (TOP-REAL n)),1))) is functional non empty non proper open closed dense non boundary complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of ((TOP-REAL n) | (cl_Ball ((0. (TOP-REAL n)),1))))
the carrier of ((TOP-REAL n) | (cl_Ball ((0. (TOP-REAL n)),1))) is functional non empty complex-functions-membered ext-real-functions-membered real-functions-membered set
K19( the carrier of ((TOP-REAL n) | (cl_Ball ((0. (TOP-REAL n)),1)))) is non empty set
K20( the carrier of ((TOP-REAL n) | TN), the carrier of ((TOP-REAL n) | (cl_Ball ((0. (TOP-REAL n)),1)))) is Relation-like set
K19(K20( the carrier of ((TOP-REAL n) | TN), the carrier of ((TOP-REAL n) | (cl_Ball ((0. (TOP-REAL n)),1))))) is non empty set
H / 2 is V21() real ext-real Element of REAL
H * (2 ") is V21() real ext-real set
GA is Relation-like the carrier of ((TOP-REAL n) | TN) -defined the carrier of ((TOP-REAL n) | (cl_Ball ((0. (TOP-REAL n)),1))) -valued Function-like V14( the carrier of ((TOP-REAL n) | TN)) quasi_total Function-yielding V275() complex-functions-valued ext-real-functions-valued real-functions-valued Element of K19(K20( the carrier of ((TOP-REAL n) | TN), the carrier of ((TOP-REAL n) | (cl_Ball ((0. (TOP-REAL n)),1)))))
x is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
G1 . x is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
U is functional non empty complex-functions-membered ext-real-functions-membered real-functions-membered a_neighborhood of G1 . x
G . x is Relation-like Function-like V137() V138() V139() set
s /\ U is functional complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
0TRn is Relation-like Function-like V137() V138() V139() Element of the carrier of ((TOP-REAL n) | s)
B is functional non empty complex-functions-membered ext-real-functions-membered real-functions-membered a_neighborhood of 0TRn
G .: B is functional non empty complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
Bx is functional complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
y is functional non empty complex-functions-membered ext-real-functions-membered real-functions-membered a_neighborhood of x
G1 .: y is functional non empty complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
Int U is functional open complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
0TRn is Relation-like Function-like V137() V138() V139() Element of the carrier of (Euclid n)
r is V21() real ext-real set
Ball (0TRn,r) is functional complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (Euclid n))
r * (H / 2) is V21() real ext-real Element of REAL
Ball (0TRn,(r * (H / 2))) is functional complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (Euclid n))
B is functional complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
Int B is functional open complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
Bx is functional non empty complex-functions-membered ext-real-functions-membered real-functions-membered a_neighborhood of x
G1 .: Bx is functional non empty complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
y is set
p is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
|.p.| is V21() real ext-real non negative Element of REAL
(H / 2) / |.p.| is V21() real ext-real Element of REAL
|.p.| " is V21() real ext-real non negative set
(H / 2) * (|.p.| ") is V21() real ext-real set
((H / 2) / |.p.|) * p is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368(p,((H / 2) / |.p.|)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
abs ((H / 2) / |.p.|) is V21() real ext-real Element of REAL
|.(((H / 2) / |.p.|) * p).| is V21() real ext-real non negative Element of REAL
((H / 2) / |.p.|) * |.p.| is V21() real ext-real Element of REAL
|.p.| / |.p.| is V21() real ext-real non negative Element of REAL
|.p.| * (|.p.| ") is V21() real ext-real non negative set
(H / 2) * (|.p.| / |.p.|) is V21() real ext-real Element of REAL
(H / 2) * 1 is V21() real ext-real Element of REAL
(((H / 2) / |.p.|) * p) - (0. (TOP-REAL n)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
- (0. (TOP-REAL n)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K364((0. (TOP-REAL n))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K246((TOP-REAL n),(((H / 2) / |.p.|) * p),(- (0. (TOP-REAL n)))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
the U6 of (TOP-REAL n) is Relation-like K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)) -defined the carrier of (TOP-REAL n) -valued Function-like non empty V14(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n))) quasi_total Function-yielding V275() complex-functions-valued ext-real-functions-valued real-functions-valued Element of K19(K20(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)), the carrier of (TOP-REAL n)))
K20(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)), the carrier of (TOP-REAL n)) is Relation-like non empty set
K19(K20(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)), the carrier of (TOP-REAL n))) is non empty set
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),(((H / 2) / |.p.|) * p),(- (0. (TOP-REAL n)))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362((((H / 2) / |.p.|) * p),(- (0. (TOP-REAL n)))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K366((((H / 2) / |.p.|) * p),(0. (TOP-REAL n))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
|.((((H / 2) / |.p.|) * p) - (0. (TOP-REAL n))).| is V21() real ext-real non negative Element of REAL
Ball ((0. (TOP-REAL n)),H) is functional convex open bounded complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
{ b₁ where b₁ is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n) : not H <= |.(b₁ - (0. (TOP-REAL n))).| } is set
halfline ((0. (TOP-REAL n)),p) is functional non empty convex closed complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
{ (((1 - b₁) * (0. (TOP-REAL n))) + (b₁ * p)) where b₁ is V21() real ext-real Element of REAL : 0 <= b₁ } is set
TN /\ (halfline ((0. (TOP-REAL n)),p)) is functional convex complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
hx is functional complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (Euclid n))
F is functional complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (Euclid n))
(Fr TN) /\ (halfline ((0. (TOP-REAL n)),p)) is functional closed complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
w is Relation-like Function-like V137() V138() V139() Element of the carrier of (Euclid n)
H1B . p is Relation-like Function-like V137() V138() V139() set
G . p is Relation-like Function-like V137() V138() V139() set
Hp is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
|.Hp.| is V21() real ext-real non negative Element of REAL
1 / |.Hp.| is V21() real ext-real non negative Element of REAL
|.Hp.| " is V21() real ext-real non negative set
1 * (|.Hp.| ") is V21() real ext-real non negative set
(1 / |.Hp.|) * p is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368(p,(1 / |.Hp.|)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
{Hp} is functional non empty V12() V32() 1 -element closed bounded compact complex-functions-membered ext-real-functions-membered real-functions-membered affinely-independent Element of K19( the carrier of (TOP-REAL n))
dist (0TRn,w) is V21() real ext-real non negative Element of REAL
(0. (TOP-REAL n)) - Hp is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
- Hp is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K364(Hp) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K246((TOP-REAL n),(0. (TOP-REAL n)),(- Hp)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),(0. (TOP-REAL n)),(- Hp)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362((0. (TOP-REAL n)),(- Hp)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K366((0. (TOP-REAL n)),Hp) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
|.((0. (TOP-REAL n)) - Hp).| is V21() real ext-real non negative Element of REAL
|.(- Hp).| is V21() real ext-real non negative Element of REAL
|.Hp.| * p is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368(p,|.Hp.|) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
G . (|.Hp.| * p) is Relation-like Function-like V137() V138() V139() set
G1 . (|.Hp.| * p) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
abs |.Hp.| is V21() real ext-real Element of REAL
Ball ((0. (TOP-REAL n)),(r * (H / 2))) is functional convex open bounded complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
{ b₁ where b₁ is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n) : not r * (H / 2) <= |.(b₁ - (0. (TOP-REAL n))).| } is set
|.(|.Hp.| * p).| is V21() real ext-real non negative Element of REAL
|.Hp.| * |.p.| is V21() real ext-real non negative Element of REAL
dom G1 is functional non empty complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
x is set
G1 . x is Relation-like Function-like V137() V138() V139() set
Ball (0TRn,H) is functional complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (Euclid n))
pp is Relation-like Function-like V137() V138() V139() Element of the carrier of (Euclid n)
dist (0TRn,pp) is V21() real ext-real non negative Element of REAL
(0. (TOP-REAL n)) - (((H / 2) / |.p.|) * p) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
- (((H / 2) / |.p.|) * p) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K364((((H / 2) / |.p.|) * p)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K246((TOP-REAL n),(0. (TOP-REAL n)),(- (((H / 2) / |.p.|) * p))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),(0. (TOP-REAL n)),(- (((H / 2) / |.p.|) * p))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362((0. (TOP-REAL n)),(- (((H / 2) / |.p.|) * p))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K366((0. (TOP-REAL n)),(((H / 2) / |.p.|) * p)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
|.((0. (TOP-REAL n)) - (((H / 2) / |.p.|) * p)).| is V21() real ext-real non negative Element of REAL
|.(- (((H / 2) / |.p.|) * p)).| is V21() real ext-real non negative Element of REAL
(H / 2) / |.Hp.| is V21() real ext-real Element of REAL
(H / 2) * (|.Hp.| ") is V21() real ext-real set
r * ((H / 2) / |.Hp.|) is V21() real ext-real Element of REAL
r * 1 is V21() real ext-real Element of REAL
(r * (H / 2)) / |.Hp.| is V21() real ext-real Element of REAL
(r * (H / 2)) * (|.Hp.| ") is V21() real ext-real set
p - (0. (TOP-REAL n)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K246((TOP-REAL n),p,(- (0. (TOP-REAL n)))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),p,(- (0. (TOP-REAL n)))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362(p,(- (0. (TOP-REAL n)))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K366(p,(0. (TOP-REAL n))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
|.(p - (0. (TOP-REAL n))).| is V21() real ext-real non negative Element of REAL
Ball ((0. (TOP-REAL n)),r) is functional convex open bounded complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
{ b₁ where b₁ is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n) : not r <= |.(b₁ - (0. (TOP-REAL n))).| } is set
p is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
GA .: FrA is functional complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of ((TOP-REAL n) | (cl_Ball ((0. (TOP-REAL n)),1))))
G1 .: FrA is functional complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
dom GA is functional complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of ((TOP-REAL n) | TN))
rng GA is functional complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of ((TOP-REAL n) | (cl_Ball ((0. (TOP-REAL n)),1))))
n is V21() ordinal natural real V32() cardinal ext-real non negative set
TOP-REAL n is non empty V90() V91() V160() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V188() TopSpace-like T_0 T_1 T_2 strict add-continuous Mult-continuous V310() V311() finite-dimensional RLTopStruct
the carrier of (TOP-REAL n) is functional non empty complex-functions-membered ext-real-functions-membered real-functions-membered set
T is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
cB is V21() real ext-real set
cl_Ball (T,cB) is functional convex closed complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
K19( the carrier of (TOP-REAL n)) is non empty set
{ b₁ where b₁ is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n) : |.(b₁ - T).| <= cB } is set
Fr (cl_Ball (T,cB)) is functional closed boundary nowhere_dense complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
Sphere (T,cB) is functional closed complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
{ b₁ where b₁ is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n) : |.(b₁ - T).| = cB } is set
Ball (T,cB) is functional convex open complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
{ b₁ where b₁ is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n) : not cB <= |.(b₁ - T).| } is set
Ts is TopSpace-like TopStruct
the carrier of Ts is set
K19( the carrier of Ts) is non empty set
(Ball (T,cB)) \/ (Sphere (T,cB)) is functional complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
F is Element of K19( the carrier of Ts)
Int F is open Element of K19( the carrier of Ts)
N is set
TN is functional complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
h is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
H is non empty V21() real ext-real positive non negative set
Ball (h,H) is functional non empty convex open complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
{ b₁ where b₁ is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n) : not H <= |.(b₁ - h).| } is set
h - T is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
- T is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K364(T) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K246((TOP-REAL n),h,(- T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
the U6 of (TOP-REAL n) is Relation-like K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)) -defined the carrier of (TOP-REAL n) -valued Function-like non empty V14(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n))) quasi_total Function-yielding V275() complex-functions-valued ext-real-functions-valued real-functions-valued Element of K19(K20(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)), the carrier of (TOP-REAL n)))
K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)) is Relation-like non empty set
K20(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)), the carrier of (TOP-REAL n)) is Relation-like non empty set
K19(K20(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)), the carrier of (TOP-REAL n))) is non empty set
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),h,(- T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362(h,(- T)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K366(h,T) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
|.(h - T).| is V21() real ext-real non negative Element of REAL
H / 2 is non empty V21() real ext-real positive non negative Element of REAL
H * (2 ") is non empty V21() real ext-real positive non negative set
(H / 2) / cB is V21() real ext-real Element of REAL
cB " is V21() real ext-real set
(H / 2) * (cB ") is V21() real ext-real set
((H / 2) / cB) * (h - T) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368((h - T),((H / 2) / cB)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
abs ((H / 2) / cB) is V21() real ext-real Element of REAL
(((H / 2) / cB) * (h - T)) + h is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),(((H / 2) / cB) * (h - T)),h) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362((((H / 2) / cB) * (h - T)),h) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
((((H / 2) / cB) * (h - T)) + h) - T is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K246((TOP-REAL n),((((H / 2) / cB) * (h - T)) + h),(- T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),((((H / 2) / cB) * (h - T)) + h),(- T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362(((((H / 2) / cB) * (h - T)) + h),(- T)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K366(((((H / 2) / cB) * (h - T)) + h),T) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
(((H / 2) / cB) * (h - T)) + (h - T) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),(((H / 2) / cB) * (h - T)),(h - T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362((((H / 2) / cB) * (h - T)),(h - T)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
f is V21() real ext-real Element of REAL
f * (h - T) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368((h - T),f) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
(((H / 2) / cB) * (h - T)) + (f * (h - T)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),(((H / 2) / cB) * (h - T)),(f * (h - T))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362((((H / 2) / cB) * (h - T)),(f * (h - T))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
((H / 2) / cB) + f is V21() real ext-real Element of REAL
(((H / 2) / cB) + f) * (h - T) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368((h - T),(((H / 2) / cB) + f)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
((((H / 2) / cB) * (h - T)) + h) - h is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
- h is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K364(h) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K246((TOP-REAL n),((((H / 2) / cB) * (h - T)) + h),(- h)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),((((H / 2) / cB) * (h - T)) + h),(- h)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362(((((H / 2) / cB) * (h - T)) + h),(- h)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K366(((((H / 2) / cB) * (h - T)) + h),h) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
|.(((((H / 2) / cB) * (h - T)) + h) - h).| is V21() real ext-real non negative Element of REAL
h - h is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K246((TOP-REAL n),h,(- h)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),h,(- h)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362(h,(- h)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K366(h,h) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
(((H / 2) / cB) * (h - T)) + (h - h) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),(((H / 2) / cB) * (h - T)),(h - h)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362((((H / 2) / cB) * (h - T)),(h - h)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
|.((((H / 2) / cB) * (h - T)) + (h - h)).| is V21() real ext-real non negative Element of REAL
0. (TOP-REAL n) is Relation-like Function-like n -element V48( TOP-REAL n) V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
the ZeroF of (TOP-REAL n) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
(((H / 2) / cB) * (h - T)) + (0. (TOP-REAL n)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),(((H / 2) / cB) * (h - T)),(0. (TOP-REAL n))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362((((H / 2) / cB) * (h - T)),(0. (TOP-REAL n))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
|.((((H / 2) / cB) * (h - T)) + (0. (TOP-REAL n))).| is V21() real ext-real non negative Element of REAL
|.(((H / 2) / cB) * (h - T)).| is V21() real ext-real non negative Element of REAL
((H / 2) / cB) * cB is V21() real ext-real Element of REAL
cB / cB is V21() real ext-real Element of COMPLEX
cB * (cB ") is V21() real ext-real set
((H / 2) / cB) + (cB / cB) is V21() real ext-real Element of REAL
(H / 2) + cB is V21() real ext-real Element of REAL
((H / 2) + cB) / cB is V21() real ext-real Element of REAL
((H / 2) + cB) * (cB ") is V21() real ext-real set
{} + cB is V21() real ext-real set
abs (((H / 2) + cB) / cB) is V21() real ext-real Element of REAL
|.(((((H / 2) / cB) * (h - T)) + h) - T).| is V21() real ext-real non negative Element of REAL
(((H / 2) + cB) / cB) * cB is V21() real ext-real Element of REAL
(cl_Ball (T,cB)) \ (Ball (T,cB)) is functional complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
n is V21() ordinal natural real V30() V31() V32() cardinal ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered Element of NAT
TOP-REAL n is non empty V90() V91() V160() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V188() TopSpace-like T_0 T_1 T_2 strict add-continuous Mult-continuous V310() V311() finite-dimensional RLTopStruct
the carrier of (TOP-REAL n) is functional non empty complex-functions-membered ext-real-functions-membered real-functions-membered set
K19( the carrier of (TOP-REAL n)) is non empty set
T is functional bounded complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
cB is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
cB + T is functional complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
Euclid n is non empty strict Reflexive discerning V65() triangle V310() V311() MetrStruct
the carrier of (Euclid n) is functional non empty complex-functions-membered ext-real-functions-membered real-functions-membered set
K19( the carrier of (Euclid n)) is non empty set
A is functional bounded complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (Euclid n))
Ts is V21() real ext-real Element of REAL
FR is functional complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (Euclid n))
{ (cB + b₁) where b₁ is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n) : b₁ in T } is set
F is Relation-like Function-like V137() V138() V139() Element of the carrier of (Euclid n)
N is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
cB + N is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
the U6 of (TOP-REAL n) is Relation-like K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)) -defined the carrier of (TOP-REAL n) -valued Function-like non empty V14(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n))) quasi_total Function-yielding V275() complex-functions-valued ext-real-functions-valued real-functions-valued Element of K19(K20(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)), the carrier of (TOP-REAL n)))
K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)) is Relation-like non empty set
K20(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)), the carrier of (TOP-REAL n)) is Relation-like non empty set
K19(K20(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)), the carrier of (TOP-REAL n))) is non empty set
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),cB,N) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362(cB,N) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
f is Relation-like Function-like V137() V138() V139() Element of the carrier of (Euclid n)
TN is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
cB + TN is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),cB,TN) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362(cB,TN) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
(cB + N) - (cB + TN) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
- (cB + TN) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K364((cB + TN)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K246((TOP-REAL n),(cB + N),(- (cB + TN))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),(cB + N),(- (cB + TN))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362((cB + N),(- (cB + TN))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K366((cB + N),(cB + TN)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
(cB + N) - cB is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
- cB is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K364(cB) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K246((TOP-REAL n),(cB + N),(- cB)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),(cB + N),(- cB)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362((cB + N),(- cB)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K366((cB + N),cB) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
((cB + N) - cB) - TN is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
- TN is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K364(TN) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K246((TOP-REAL n),((cB + N) - cB),(- TN)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),((cB + N) - cB),(- TN)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362(((cB + N) - cB),(- TN)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K366(((cB + N) - cB),TN) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
N - TN is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K246((TOP-REAL n),N,(- TN)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),N,(- TN)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362(N,(- TN)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K366(N,TN) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
dist (F,f) is V21() real ext-real non negative Element of REAL
|.(N - TN).| is V21() real ext-real non negative Element of REAL
h is Relation-like Function-like V137() V138() V139() Element of the carrier of (Euclid n)
H is Relation-like Function-like V137() V138() V139() Element of the carrier of (Euclid n)
dist (h,H) is V21() real ext-real non negative Element of REAL
n is V21() ordinal natural real V30() V31() V32() cardinal ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered Element of NAT
TOP-REAL n is non empty V90() V91() V160() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V188() TopSpace-like T_0 T_1 T_2 strict add-continuous Mult-continuous V310() V311() finite-dimensional RLTopStruct
the carrier of (TOP-REAL n) is functional non empty complex-functions-membered ext-real-functions-membered real-functions-membered set
K19( the carrier of (TOP-REAL n)) is non empty set
0. (TOP-REAL n) is Relation-like Function-like n -element V48( TOP-REAL n) V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
the ZeroF of (TOP-REAL n) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
Tdisk ((0. (TOP-REAL n)),1) is non empty TopSpace-like T_0 T_1 T_2 V307(n) V310() V311() SubSpace of TOP-REAL n
cl_Ball ((0. (TOP-REAL n)),1) is functional non empty convex closed bounded compact complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
{ b₁ where b₁ is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n) : |.(b₁ - (0. (TOP-REAL n))).| <= 1 } is set
(TOP-REAL n) | (cl_Ball ((0. (TOP-REAL n)),1)) is non empty strict TopSpace-like T_0 T_1 T_2 compact V310() V311() SubSpace of TOP-REAL n
the carrier of (Tdisk ((0. (TOP-REAL n)),1)) is functional non empty complex-functions-membered ext-real-functions-membered real-functions-membered set
Sphere ((0. (TOP-REAL n)),1) is functional closed bounded compact complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
{ b₁ where b₁ is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n) : |.(b₁ - (0. (TOP-REAL n))).| = 1 } is set
cB is functional convex complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
(TOP-REAL n) | cB is strict TopSpace-like T_0 T_1 T_2 V310() V311() SubSpace of TOP-REAL n
the carrier of ((TOP-REAL n) | cB) is functional complex-functions-membered ext-real-functions-membered real-functions-membered set
K20( the carrier of ((TOP-REAL n) | cB), the carrier of (Tdisk ((0. (TOP-REAL n)),1))) is Relation-like set
K19(K20( the carrier of ((TOP-REAL n) | cB), the carrier of (Tdisk ((0. (TOP-REAL n)),1)))) is non empty set
Fr cB is functional closed complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
Int cB is functional convex open complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
S is set
{(0. (TOP-REAL n))} is functional non empty V12() V32() 1 -element closed bounded compact complex-functions-membered ext-real-functions-membered real-functions-membered affinely-independent Element of K19( the carrier of (TOP-REAL n))
id ((TOP-REAL n) | cB) is Relation-like the carrier of ((TOP-REAL n) | cB) -defined the carrier of ((TOP-REAL n) | cB) -valued Function-like one-to-one V14( the carrier of ((TOP-REAL n) | cB)) quasi_total onto bijective continuous Function-yielding V275() complex-functions-valued ext-real-functions-valued real-functions-valued being_homeomorphism Element of K19(K20( the carrier of ((TOP-REAL n) | cB), the carrier of ((TOP-REAL n) | cB)))
K20( the carrier of ((TOP-REAL n) | cB), the carrier of ((TOP-REAL n) | cB)) is Relation-like set
K19(K20( the carrier of ((TOP-REAL n) | cB), the carrier of ((TOP-REAL n) | cB))) is non empty set
id the carrier of ((TOP-REAL n) | cB) is Relation-like the carrier of ((TOP-REAL n) | cB) -defined the carrier of ((TOP-REAL n) | cB) -valued Function-like one-to-one V14( the carrier of ((TOP-REAL n) | cB)) quasi_total Function-yielding V275() complex-functions-valued ext-real-functions-valued real-functions-valued Element of K19(K20( the carrier of ((TOP-REAL n) | cB), the carrier of ((TOP-REAL n) | cB)))
Ts is Relation-like the carrier of ((TOP-REAL n) | cB) -defined the carrier of (Tdisk ((0. (TOP-REAL n)),1)) -valued Function-like V14( the carrier of ((TOP-REAL n) | cB)) quasi_total Function-yielding V275() complex-functions-valued ext-real-functions-valued real-functions-valued Element of K19(K20( the carrier of ((TOP-REAL n) | cB), the carrier of (Tdisk ((0. (TOP-REAL n)),1))))
Ts .: (Fr cB) is functional complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (Tdisk ((0. (TOP-REAL n)),1)))
K19( the carrier of (Tdisk ((0. (TOP-REAL n)),1))) is non empty set
cB \ (Int cB) is functional complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
|.(0. (TOP-REAL n)).| is V21() real ext-real non negative Element of REAL
A is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
- A is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K364(A) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
transl ((- A),(TOP-REAL n)) is Relation-like the carrier of (TOP-REAL n) -defined the carrier of (TOP-REAL n) -valued Function-like one-to-one non empty V14( the carrier of (TOP-REAL n)) quasi_total onto bijective continuous Function-yielding V275() complex-functions-valued ext-real-functions-valued real-functions-valued being_homeomorphism Element of K19(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)))
K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)) is Relation-like non empty set
K19(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n))) is non empty set
(transl ((- A),(TOP-REAL n))) .: cB is functional complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
(- A) + cB is functional complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
0* n is Relation-like NAT -defined REAL -valued Function-like n -element V76() V137() V138() V139() Element of REAL n
REAL n is functional non empty V78() complex-functions-membered ext-real-functions-membered real-functions-membered M10( REAL )
(TOP-REAL n) | ((transl ((- A),(TOP-REAL n))) .: cB) is strict TopSpace-like T_0 T_1 T_2 V310() V311() SubSpace of TOP-REAL n
the carrier of ((TOP-REAL n) | ((transl ((- A),(TOP-REAL n))) .: cB)) is functional complex-functions-membered ext-real-functions-membered real-functions-membered set
K20( the carrier of ((TOP-REAL n) | cB), the carrier of ((TOP-REAL n) | ((transl ((- A),(TOP-REAL n))) .: cB))) is Relation-like set
K19(K20( the carrier of ((TOP-REAL n) | cB), the carrier of ((TOP-REAL n) | ((transl ((- A),(TOP-REAL n))) .: cB)))) is non empty set
(transl ((- A),(TOP-REAL n))) | cB is Relation-like the carrier of (TOP-REAL n) -defined cB -defined the carrier of (TOP-REAL n) -defined the carrier of (TOP-REAL n) -valued Function-like Function-yielding V275() complex-functions-valued ext-real-functions-valued real-functions-valued Element of K19(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)))
F is Relation-like the carrier of ((TOP-REAL n) | cB) -defined the carrier of ((TOP-REAL n) | ((transl ((- A),(TOP-REAL n))) .: cB)) -valued Function-like quasi_total Function-yielding V275() complex-functions-valued ext-real-functions-valued real-functions-valued Element of K19(K20( the carrier of ((TOP-REAL n) | cB), the carrier of ((TOP-REAL n) | ((transl ((- A),(TOP-REAL n))) .: cB))))
F .: (Int cB) is functional complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of ((TOP-REAL n) | ((transl ((- A),(TOP-REAL n))) .: cB)))
K19( the carrier of ((TOP-REAL n) | ((transl ((- A),(TOP-REAL n))) .: cB))) is non empty set
(transl ((- A),(TOP-REAL n))) .: (Int cB) is functional complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
(- A) + A is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
the U6 of (TOP-REAL n) is Relation-like K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)) -defined the carrier of (TOP-REAL n) -valued Function-like non empty V14(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n))) quasi_total Function-yielding V275() complex-functions-valued ext-real-functions-valued real-functions-valued Element of K19(K20(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)), the carrier of (TOP-REAL n)))
K20(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)), the carrier of (TOP-REAL n)) is Relation-like non empty set
K19(K20(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)), the carrier of (TOP-REAL n))) is non empty set
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),(- A),A) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362((- A),A) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
{ ((- A) + b₁) where b₁ is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n) : b₁ in Int cB } is set
Int ((transl ((- A),(TOP-REAL n))) .: cB) is functional open complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
(- A) + (Int cB) is functional open complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
K20( the carrier of ((TOP-REAL n) | ((transl ((- A),(TOP-REAL n))) .: cB)), the carrier of (Tdisk ((0. (TOP-REAL n)),1))) is Relation-like set
K19(K20( the carrier of ((TOP-REAL n) | ((transl ((- A),(TOP-REAL n))) .: cB)), the carrier of (Tdisk ((0. (TOP-REAL n)),1)))) is non empty set
Fr ((transl ((- A),(TOP-REAL n))) .: cB) is functional closed complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
f is Relation-like the carrier of ((TOP-REAL n) | ((transl ((- A),(TOP-REAL n))) .: cB)) -defined the carrier of (Tdisk ((0. (TOP-REAL n)),1)) -valued Function-like V14( the carrier of ((TOP-REAL n) | ((transl ((- A),(TOP-REAL n))) .: cB))) quasi_total Function-yielding V275() complex-functions-valued ext-real-functions-valued real-functions-valued Element of K19(K20( the carrier of ((TOP-REAL n) | ((transl ((- A),(TOP-REAL n))) .: cB)), the carrier of (Tdisk ((0. (TOP-REAL n)),1))))
f .: (Fr ((transl ((- A),(TOP-REAL n))) .: cB)) is functional complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (Tdisk ((0. (TOP-REAL n)),1)))
K19( the carrier of (Tdisk ((0. (TOP-REAL n)),1))) is non empty set
f * F is Relation-like the carrier of ((TOP-REAL n) | cB) -defined the carrier of (Tdisk ((0. (TOP-REAL n)),1)) -valued Function-like Function-yielding V275() complex-functions-valued ext-real-functions-valued real-functions-valued Element of K19(K20( the carrier of ((TOP-REAL n) | cB), the carrier of (Tdisk ((0. (TOP-REAL n)),1))))
N is Relation-like the carrier of ((TOP-REAL n) | cB) -defined the carrier of (Tdisk ((0. (TOP-REAL n)),1)) -valued Function-like V14( the carrier of ((TOP-REAL n) | cB)) quasi_total Function-yielding V275() complex-functions-valued ext-real-functions-valued real-functions-valued Element of K19(K20( the carrier of ((TOP-REAL n) | cB), the carrier of (Tdisk ((0. (TOP-REAL n)),1))))
N .: (Fr cB) is functional complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (Tdisk ((0. (TOP-REAL n)),1)))
dom F is functional complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of ((TOP-REAL n) | cB))
K19( the carrier of ((TOP-REAL n) | cB)) is non empty set
[#] ((TOP-REAL n) | cB) is functional non proper open closed dense complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of ((TOP-REAL n) | cB))
rng F is functional complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of ((TOP-REAL n) | ((transl ((- A),(TOP-REAL n))) .: cB)))
[#] ((TOP-REAL n) | ((transl ((- A),(TOP-REAL n))) .: cB)) is functional non proper open closed dense complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of ((TOP-REAL n) | ((transl ((- A),(TOP-REAL n))) .: cB)))
cB \ (Int cB) is functional complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
F .: (Fr cB) is functional complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of ((TOP-REAL n) | ((transl ((- A),(TOP-REAL n))) .: cB)))
F .: cB is functional complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of ((TOP-REAL n) | ((transl ((- A),(TOP-REAL n))) .: cB)))
(F .: cB) \ (F .: (Int cB)) is functional complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of ((TOP-REAL n) | ((transl ((- A),(TOP-REAL n))) .: cB)))
((transl ((- A),(TOP-REAL n))) .: cB) \ (Int ((transl ((- A),(TOP-REAL n))) .: cB)) is functional complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
n is V21() ordinal natural real V32() cardinal ext-real non negative set
TOP-REAL n is non empty V90() V91() V160() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V188() TopSpace-like T_0 T_1 T_2 strict add-continuous Mult-continuous V310() V311() finite-dimensional RLTopStruct
the carrier of (TOP-REAL n) is functional non empty complex-functions-membered ext-real-functions-membered real-functions-membered set
K19( the carrier of (TOP-REAL n)) is non empty set
cB is functional convex complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
S is functional convex complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
(TOP-REAL n) | cB is strict TopSpace-like T_0 T_1 T_2 V310() V311() SubSpace of TOP-REAL n
the carrier of ((TOP-REAL n) | cB) is functional complex-functions-membered ext-real-functions-membered real-functions-membered set
(TOP-REAL n) | S is strict TopSpace-like T_0 T_1 T_2 V310() V311() SubSpace of TOP-REAL n
the carrier of ((TOP-REAL n) | S) is functional complex-functions-membered ext-real-functions-membered real-functions-membered set
K20( the carrier of ((TOP-REAL n) | cB), the carrier of ((TOP-REAL n) | S)) is Relation-like set
K19(K20( the carrier of ((TOP-REAL n) | cB), the carrier of ((TOP-REAL n) | S))) is non empty set
Fr cB is functional closed complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
Fr S is functional closed complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
s is V21() ordinal natural real V30() V31() V32() cardinal ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered Element of NAT
TOP-REAL s is non empty V90() V91() V160() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V188() TopSpace-like T_0 T_1 T_2 strict add-continuous Mult-continuous V310() V311() finite-dimensional RLTopStruct
0. (TOP-REAL s) is Relation-like Function-like s -element V48( TOP-REAL s) V76() V137() V138() V139() Element of the carrier of (TOP-REAL s)
the carrier of (TOP-REAL s) is functional non empty complex-functions-membered ext-real-functions-membered real-functions-membered set
the ZeroF of (TOP-REAL s) is Relation-like Function-like s -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL s)
Tdisk ((0. (TOP-REAL s)),1) is non empty TopSpace-like T_0 T_1 T_2 V307(s) V310() V311() SubSpace of TOP-REAL s
cl_Ball ((0. (TOP-REAL s)),1) is functional non empty convex closed bounded compact complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL s))
K19( the carrier of (TOP-REAL s)) is non empty set
{ b₁ where b₁ is Relation-like Function-like s -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL s) : |.(b₁ - (0. (TOP-REAL s))).| <= 1 } is set
(TOP-REAL s) | (cl_Ball ((0. (TOP-REAL s)),1)) is non empty strict TopSpace-like T_0 T_1 T_2 compact V310() V311() SubSpace of TOP-REAL s
the carrier of (Tdisk ((0. (TOP-REAL s)),1)) is functional non empty complex-functions-membered ext-real-functions-membered real-functions-membered set
K20( the carrier of ((TOP-REAL n) | cB), the carrier of (Tdisk ((0. (TOP-REAL s)),1))) is Relation-like set
K19(K20( the carrier of ((TOP-REAL n) | cB), the carrier of (Tdisk ((0. (TOP-REAL s)),1)))) is non empty set
0. (TOP-REAL n) is Relation-like Function-like n -element V48( TOP-REAL n) V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
the ZeroF of (TOP-REAL n) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
Sphere ((0. (TOP-REAL n)),1) is functional closed complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
{ b₁ where b₁ is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n) : |.(b₁ - (0. (TOP-REAL n))).| = 1 } is set
FR is Relation-like the carrier of ((TOP-REAL n) | cB) -defined the carrier of (Tdisk ((0. (TOP-REAL s)),1)) -valued Function-like V14( the carrier of ((TOP-REAL n) | cB)) quasi_total Function-yielding V275() complex-functions-valued ext-real-functions-valued real-functions-valued Element of K19(K20( the carrier of ((TOP-REAL n) | cB), the carrier of (Tdisk ((0. (TOP-REAL s)),1))))
FR .: (Fr cB) is functional complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (Tdisk ((0. (TOP-REAL s)),1)))
K19( the carrier of (Tdisk ((0. (TOP-REAL s)),1))) is non empty set
K20( the carrier of ((TOP-REAL n) | S), the carrier of (Tdisk ((0. (TOP-REAL s)),1))) is Relation-like set
K19(K20( the carrier of ((TOP-REAL n) | S), the carrier of (Tdisk ((0. (TOP-REAL s)),1)))) is non empty set
Ts is Relation-like the carrier of ((TOP-REAL n) | S) -defined the carrier of (Tdisk ((0. (TOP-REAL s)),1)) -valued Function-like V14( the carrier of ((TOP-REAL n) | S)) quasi_total Function-yielding V275() complex-functions-valued ext-real-functions-valued real-functions-valued Element of K19(K20( the carrier of ((TOP-REAL n) | S), the carrier of (Tdisk ((0. (TOP-REAL s)),1))))
Ts .: (Fr S) is functional complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (Tdisk ((0. (TOP-REAL s)),1)))
Ts /" is Relation-like the carrier of (Tdisk ((0. (TOP-REAL s)),1)) -defined the carrier of ((TOP-REAL n) | S) -valued Function-like quasi_total Function-yielding V275() complex-functions-valued ext-real-functions-valued real-functions-valued Element of K19(K20( the carrier of (Tdisk ((0. (TOP-REAL s)),1)), the carrier of ((TOP-REAL n) | S)))
K20( the carrier of (Tdisk ((0. (TOP-REAL s)),1)), the carrier of ((TOP-REAL n) | S)) is Relation-like set
K19(K20( the carrier of (Tdisk ((0. (TOP-REAL s)),1)), the carrier of ((TOP-REAL n) | S))) is non empty set
(Ts /") * FR is Relation-like the carrier of ((TOP-REAL n) | cB) -defined the carrier of ((TOP-REAL n) | S) -valued Function-like quasi_total Function-yielding V275() complex-functions-valued ext-real-functions-valued real-functions-valued Element of K19(K20( the carrier of ((TOP-REAL n) | cB), the carrier of ((TOP-REAL n) | S)))
F is Relation-like the carrier of ((TOP-REAL n) | cB) -defined the carrier of ((TOP-REAL n) | S) -valued Function-like quasi_total Function-yielding V275() complex-functions-valued ext-real-functions-valued real-functions-valued Element of K19(K20( the carrier of ((TOP-REAL n) | cB), the carrier of ((TOP-REAL n) | S)))
F .: (Fr cB) is functional complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of ((TOP-REAL n) | S))
K19( the carrier of ((TOP-REAL n) | S)) is non empty set
rng Ts is functional complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (Tdisk ((0. (TOP-REAL s)),1)))
[#] (Tdisk ((0. (TOP-REAL s)),1)) is functional non empty non proper open closed dense non boundary complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (Tdisk ((0. (TOP-REAL s)),1)))
dom Ts is functional complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of ((TOP-REAL n) | S))
[#] ((TOP-REAL n) | S) is functional non proper open closed dense complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of ((TOP-REAL n) | S))
(Ts /") .: (Sphere ((0. (TOP-REAL n)),1)) is functional complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of ((TOP-REAL n) | S))
Ts " (Sphere ((0. (TOP-REAL n)),1)) is functional complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of ((TOP-REAL n) | S))
n is V21() ordinal natural real V32() cardinal ext-real non negative set
TOP-REAL n is non empty V90() V91() V160() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V188() TopSpace-like T_0 T_1 T_2 strict add-continuous Mult-continuous V310() V311() finite-dimensional RLTopStruct
the carrier of (TOP-REAL n) is functional non empty complex-functions-membered ext-real-functions-membered real-functions-membered set
K19( the carrier of (TOP-REAL n)) is non empty set
{} (TOP-REAL n) is Relation-like non-empty empty-yielding RAT -valued Function-like one-to-one constant functional empty proper V21() ordinal natural real V32() V33() V36() cardinal {} -element ext-real non positive non negative V137() V138() V139() V140() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V153() open closed V254( TOP-REAL n) circled bounded boundary nowhere_dense compact Function-yielding V275() complex-functions-membered ext-real-functions-membered real-functions-membered rational-functions-membered integer-functions-membered natural-functions-membered complex-functions-valued ext-real-functions-valued real-functions-valued rational-functions-valued integer-functions-valued natural-functions-valued affinely-independent Element of K19( the carrier of (TOP-REAL n))
[#] (TOP-REAL n) is functional non empty non proper non proper convex open open closed closed dense dense non boundary non boundary complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
Affin ([#] (TOP-REAL n)) is functional non empty closed complex-functions-membered ext-real-functions-membered real-functions-membered Affine Element of K19( the carrier of (TOP-REAL n))
cB is functional V32() closed compact complex-functions-membered ext-real-functions-membered real-functions-membered affinely-independent Element of K19( the carrier of (TOP-REAL n))
Affin cB is functional closed complex-functions-membered ext-real-functions-membered real-functions-membered Affine Element of K19( the carrier of (TOP-REAL n))
S is non empty RLSStruct
the carrier of S is non empty set
K19( the carrier of S) is non empty set
s is Element of K19( the carrier of S)
Int s is Element of K19( the carrier of S)
FR is functional complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
Int FR is functional open complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
conv cB is functional convex convex closed compact complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
Int (conv cB) is functional convex open complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
Ts is functional convex complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
(TOP-REAL n) | Ts is strict TopSpace-like T_0 T_1 T_2 V310() V311() SubSpace of TOP-REAL n
the carrier of ((TOP-REAL n) | Ts) is functional complex-functions-membered ext-real-functions-membered real-functions-membered set
K20( the carrier of ((TOP-REAL n) | Ts), the carrier of ((TOP-REAL n) | Ts)) is Relation-like set
K19(K20( the carrier of ((TOP-REAL n) | Ts), the carrier of ((TOP-REAL n) | Ts))) is non empty set
F is Relation-like the carrier of ((TOP-REAL n) | Ts) -defined the carrier of ((TOP-REAL n) | Ts) -valued Function-like V14( the carrier of ((TOP-REAL n) | Ts)) quasi_total continuous Function-yielding V275() complex-functions-valued ext-real-functions-valued real-functions-valued Element of K19(K20( the carrier of ((TOP-REAL n) | Ts), the carrier of ((TOP-REAL n) | Ts)))
dim (TOP-REAL n) is V21() ordinal natural real V30() V31() V32() cardinal ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered Element of NAT
card cB is V21() ordinal natural real V30() V31() V32() cardinal ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered Element of omega
n + 1 is non empty V21() ordinal natural real V32() cardinal ext-real positive non negative Element of REAL
(TOP-REAL n) | (conv cB) is strict TopSpace-like T_0 T_1 T_2 compact V310() V311() SubSpace of TOP-REAL n
the carrier of ((TOP-REAL n) | (conv cB)) is functional complex-functions-membered ext-real-functions-membered real-functions-membered set
K20( the carrier of ((TOP-REAL n) | Ts), the carrier of ((TOP-REAL n) | (conv cB))) is Relation-like set
K19(K20( the carrier of ((TOP-REAL n) | Ts), the carrier of ((TOP-REAL n) | (conv cB)))) is non empty set
Fr Ts is functional closed complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
Fr (conv cB) is functional closed boundary nowhere_dense complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
f is Relation-like the carrier of ((TOP-REAL n) | Ts) -defined the carrier of ((TOP-REAL n) | (conv cB)) -valued Function-like quasi_total Function-yielding V275() complex-functions-valued ext-real-functions-valued real-functions-valued Element of K19(K20( the carrier of ((TOP-REAL n) | Ts), the carrier of ((TOP-REAL n) | (conv cB))))
f .: (Fr Ts) is functional complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of ((TOP-REAL n) | (conv cB)))
K19( the carrier of ((TOP-REAL n) | (conv cB))) is non empty set
K20( the carrier of ((TOP-REAL n) | (conv cB)), the carrier of ((TOP-REAL n) | (conv cB))) is Relation-like set
K19(K20( the carrier of ((TOP-REAL n) | (conv cB)), the carrier of ((TOP-REAL n) | (conv cB)))) is non empty set
f /" is Relation-like the carrier of ((TOP-REAL n) | (conv cB)) -defined the carrier of ((TOP-REAL n) | Ts) -valued Function-like quasi_total Function-yielding V275() complex-functions-valued ext-real-functions-valued real-functions-valued Element of K19(K20( the carrier of ((TOP-REAL n) | (conv cB)), the carrier of ((TOP-REAL n) | Ts)))
K20( the carrier of ((TOP-REAL n) | (conv cB)), the carrier of ((TOP-REAL n) | Ts)) is Relation-like set
K19(K20( the carrier of ((TOP-REAL n) | (conv cB)), the carrier of ((TOP-REAL n) | Ts))) is non empty set
F * (f /") is Relation-like the carrier of ((TOP-REAL n) | (conv cB)) -defined the carrier of ((TOP-REAL n) | Ts) -valued Function-like quasi_total Function-yielding V275() complex-functions-valued ext-real-functions-valued real-functions-valued Element of K19(K20( the carrier of ((TOP-REAL n) | (conv cB)), the carrier of ((TOP-REAL n) | Ts)))
f * (F * (f /")) is Relation-like the carrier of ((TOP-REAL n) | (conv cB)) -defined the carrier of ((TOP-REAL n) | (conv cB)) -valued Function-like Function-yielding V275() complex-functions-valued ext-real-functions-valued real-functions-valued Element of K19(K20( the carrier of ((TOP-REAL n) | (conv cB)), the carrier of ((TOP-REAL n) | (conv cB))))
N is Relation-like the carrier of ((TOP-REAL n) | (conv cB)) -defined the carrier of ((TOP-REAL n) | (conv cB)) -valued Function-like V14( the carrier of ((TOP-REAL n) | (conv cB))) quasi_total Function-yielding V275() complex-functions-valued ext-real-functions-valued real-functions-valued Element of K19(K20( the carrier of ((TOP-REAL n) | (conv cB)), the carrier of ((TOP-REAL n) | (conv cB))))
dom N is functional complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of ((TOP-REAL n) | (conv cB)))
TN is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
N . TN is Relation-like Function-like V137() V138() V139() set
dom (F * (f /")) is functional complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of ((TOP-REAL n) | (conv cB)))
rng f is functional complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of ((TOP-REAL n) | (conv cB)))
[#] ((TOP-REAL n) | (conv cB)) is functional non proper open closed dense complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of ((TOP-REAL n) | (conv cB)))
h is Relation-like Function-like set
h " is Relation-like Function-like set
dom h is set
H is set
h . H is set
(h ") . TN is set
(F * (f /")) . TN is Relation-like Function-like V137() V138() V139() set
F . H is Relation-like Function-like V137() V138() V139() set
f . (F . H) is Relation-like Function-like V137() V138() V139() set
dom f is functional complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of ((TOP-REAL n) | Ts))
K19( the carrier of ((TOP-REAL n) | Ts)) is non empty set
[#] ((TOP-REAL n) | Ts) is functional non proper open closed dense complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of ((TOP-REAL n) | Ts))
dom F is functional complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of ((TOP-REAL n) | Ts))
rng F is functional complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of ((TOP-REAL n) | Ts))
n is V21() ordinal natural real V32() cardinal ext-real non negative set
TOP-REAL n is non empty V90() V91() V160() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V188() TopSpace-like T_0 T_1 T_2 strict add-continuous Mult-continuous V310() V311() finite-dimensional RLTopStruct
0. (TOP-REAL n) is Relation-like Function-like n -element V48( TOP-REAL n) V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
the carrier of (TOP-REAL n) is functional non empty complex-functions-membered ext-real-functions-membered real-functions-membered set
the ZeroF of (TOP-REAL n) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
cl_Ball ((0. (TOP-REAL n)),1) is functional non empty convex closed complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
K19( the carrier of (TOP-REAL n)) is non empty set
{ b₁ where b₁ is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n) : |.(b₁ - (0. (TOP-REAL n))).| <= 1 } is set
cB is TopStruct
the carrier of cB is set
K19( the carrier of cB) is non empty set
Ball ((0. (TOP-REAL n)),1) is functional non empty convex open complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
{ b₁ where b₁ is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n) : not 1 <= |.(b₁ - (0. (TOP-REAL n))).| } is set
S is Element of K19( the carrier of cB)
Int S is Element of K19( the carrier of cB)
n is V21() ordinal natural real V30() V31() V32() cardinal ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered Element of NAT
TOP-REAL n is non empty V90() V91() V160() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V188() TopSpace-like T_0 T_1 T_2 strict add-continuous Mult-continuous V310() V311() finite-dimensional RLTopStruct
0. (TOP-REAL n) is Relation-like Function-like n -element V48( TOP-REAL n) V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
the carrier of (TOP-REAL n) is functional non empty complex-functions-membered ext-real-functions-membered real-functions-membered set
the ZeroF of (TOP-REAL n) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
Tdisk ((0. (TOP-REAL n)),1) is non empty TopSpace-like T_0 T_1 T_2 V307(n) V310() V311() SubSpace of TOP-REAL n
cl_Ball ((0. (TOP-REAL n)),1) is functional non empty convex closed bounded compact complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
K19( the carrier of (TOP-REAL n)) is non empty set
{ b₁ where b₁ is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n) : |.(b₁ - (0. (TOP-REAL n))).| <= 1 } is set
(TOP-REAL n) | (cl_Ball ((0. (TOP-REAL n)),1)) is non empty strict TopSpace-like T_0 T_1 T_2 compact V310() V311() SubSpace of TOP-REAL n
Tcircle ((0. (TOP-REAL n)),1) is TopSpace-like T_0 T_1 T_2 V310() V311() SubSpace of TOP-REAL n
Sphere ((0. (TOP-REAL n)),1) is functional closed bounded compact complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
{ b₁ where b₁ is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n) : |.(b₁ - (0. (TOP-REAL n))).| = 1 } is set
mlt ((- 1),(TOP-REAL n)) is Relation-like the carrier of (TOP-REAL n) -defined the carrier of (TOP-REAL n) -valued Function-like one-to-one non empty V14( the carrier of (TOP-REAL n)) quasi_total onto bijective continuous Function-yielding V275() complex-functions-valued ext-real-functions-valued real-functions-valued being_homeomorphism Element of K19(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)))
K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)) is Relation-like non empty set
K19(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n))) is non empty set
s is non empty TopSpace-like T_0 T_1 T_2 V310() V311() SubSpace of Tdisk ((0. (TOP-REAL n)),1)
the carrier of s is functional non empty complex-functions-membered ext-real-functions-membered real-functions-membered set
the carrier of (Tdisk ((0. (TOP-REAL n)),1)) is functional non empty complex-functions-membered ext-real-functions-membered real-functions-membered set
K20( the carrier of (Tdisk ((0. (TOP-REAL n)),1)), the carrier of s) is Relation-like non empty set
K19(K20( the carrier of (Tdisk ((0. (TOP-REAL n)),1)), the carrier of s)) is non empty set
A is Relation-like the carrier of (Tdisk ((0. (TOP-REAL n)),1)) -defined the carrier of s -valued Function-like non empty V14( the carrier of (Tdisk ((0. (TOP-REAL n)),1))) quasi_total continuous Function-yielding V275() complex-functions-valued ext-real-functions-valued real-functions-valued Element of K19(K20( the carrier of (Tdisk ((0. (TOP-REAL n)),1)), the carrier of s))
K20( the carrier of (Tdisk ((0. (TOP-REAL n)),1)), the carrier of (Tdisk ((0. (TOP-REAL n)),1))) is Relation-like non empty set
K19(K20( the carrier of (Tdisk ((0. (TOP-REAL n)),1)), the carrier of (Tdisk ((0. (TOP-REAL n)),1)))) is non empty set
FR is Relation-like the carrier of (Tdisk ((0. (TOP-REAL n)),1)) -defined the carrier of (Tdisk ((0. (TOP-REAL n)),1)) -valued Function-like non empty V14( the carrier of (Tdisk ((0. (TOP-REAL n)),1))) quasi_total Function-yielding V275() complex-functions-valued ext-real-functions-valued real-functions-valued Element of K19(K20( the carrier of (Tdisk ((0. (TOP-REAL n)),1)), the carrier of (Tdisk ((0. (TOP-REAL n)),1))))
(mlt ((- 1),(TOP-REAL n))) | (Tdisk ((0. (TOP-REAL n)),1)) is Relation-like the carrier of (Tdisk ((0. (TOP-REAL n)),1)) -defined the carrier of (TOP-REAL n) -valued Function-like non empty V14( the carrier of (Tdisk ((0. (TOP-REAL n)),1))) quasi_total continuous Function-yielding V275() complex-functions-valued ext-real-functions-valued real-functions-valued Element of K19(K20( the carrier of (Tdisk ((0. (TOP-REAL n)),1)), the carrier of (TOP-REAL n)))
K20( the carrier of (Tdisk ((0. (TOP-REAL n)),1)), the carrier of (TOP-REAL n)) is Relation-like non empty set
K19(K20( the carrier of (Tdisk ((0. (TOP-REAL n)),1)), the carrier of (TOP-REAL n))) is non empty set
((mlt ((- 1),(TOP-REAL n))) | (Tdisk ((0. (TOP-REAL n)),1))) * FR is Relation-like the carrier of (Tdisk ((0. (TOP-REAL n)),1)) -defined the carrier of (TOP-REAL n) -valued Function-like non empty V14( the carrier of (Tdisk ((0. (TOP-REAL n)),1))) quasi_total Function-yielding V275() complex-functions-valued ext-real-functions-valued real-functions-valued Element of K19(K20( the carrier of (Tdisk ((0. (TOP-REAL n)),1)), the carrier of (TOP-REAL n)))
(mlt ((- 1),(TOP-REAL n))) | the carrier of (Tdisk ((0. (TOP-REAL n)),1)) is Relation-like the carrier of (TOP-REAL n) -defined the carrier of (Tdisk ((0. (TOP-REAL n)),1)) -defined the carrier of (TOP-REAL n) -defined the carrier of (TOP-REAL n) -valued Function-like Function-yielding V275() complex-functions-valued ext-real-functions-valued real-functions-valued Element of K19(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)))
rng (((mlt ((- 1),(TOP-REAL n))) | (Tdisk ((0. (TOP-REAL n)),1))) * FR) is functional non empty complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
F is set
dom (((mlt ((- 1),(TOP-REAL n))) | (Tdisk ((0. (TOP-REAL n)),1))) * FR) is functional non empty complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (Tdisk ((0. (TOP-REAL n)),1)))
K19( the carrier of (Tdisk ((0. (TOP-REAL n)),1))) is non empty set
f is set
(((mlt ((- 1),(TOP-REAL n))) | (Tdisk ((0. (TOP-REAL n)),1))) * FR) . f is Relation-like Function-like V137() V138() V139() set
FR . f is Relation-like Function-like V137() V138() V139() set
dom ((mlt ((- 1),(TOP-REAL n))) | (Tdisk ((0. (TOP-REAL n)),1))) is functional non empty complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (Tdisk ((0. (TOP-REAL n)),1)))
dom (mlt ((- 1),(TOP-REAL n))) is functional non empty complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
dom FR is functional non empty complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (Tdisk ((0. (TOP-REAL n)),1)))
rng A is functional non empty complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of s)
K19( the carrier of s) is non empty set
N is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
|.N.| is V21() real ext-real non negative Element of REAL
- N is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K364(N) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
|.(- N).| is V21() real ext-real non negative Element of REAL
(- N) - (0. (TOP-REAL n)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
- (0. (TOP-REAL n)) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K364((0. (TOP-REAL n))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K246((TOP-REAL n),(- N),(- (0. (TOP-REAL n)))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
the U6 of (TOP-REAL n) is Relation-like K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)) -defined the carrier of (TOP-REAL n) -valued Function-like non empty V14(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n))) quasi_total Function-yielding V275() complex-functions-valued ext-real-functions-valued real-functions-valued Element of K19(K20(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)), the carrier of (TOP-REAL n)))
K20(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)), the carrier of (TOP-REAL n)) is Relation-like non empty set
K19(K20(K20( the carrier of (TOP-REAL n), the carrier of (TOP-REAL n)), the carrier of (TOP-REAL n))) is non empty set
K196( the carrier of (TOP-REAL n), the U6 of (TOP-REAL n),(- N),(- (0. (TOP-REAL n)))) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K362((- N),(- (0. (TOP-REAL n)))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
K366((- N),(0. (TOP-REAL n))) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
|.((- N) - (0. (TOP-REAL n))).| is V21() real ext-real non negative Element of REAL
((mlt ((- 1),(TOP-REAL n))) | (Tdisk ((0. (TOP-REAL n)),1))) . (FR . f) is Relation-like Function-like V137() V138() V139() set
(mlt ((- 1),(TOP-REAL n))) . (FR . f) is Relation-like Function-like V137() V138() V139() set
(- 1) * N is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368(N,(- 1)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
F is Relation-like the carrier of (Tdisk ((0. (TOP-REAL n)),1)) -defined the carrier of (Tdisk ((0. (TOP-REAL n)),1)) -valued Function-like non empty V14( the carrier of (Tdisk ((0. (TOP-REAL n)),1))) quasi_total Function-yielding V275() complex-functions-valued ext-real-functions-valued real-functions-valued Element of K19(K20( the carrier of (Tdisk ((0. (TOP-REAL n)),1)), the carrier of (Tdisk ((0. (TOP-REAL n)),1))))
f is set
dom F is functional non empty complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (Tdisk ((0. (TOP-REAL n)),1)))
K19( the carrier of (Tdisk ((0. (TOP-REAL n)),1))) is non empty set
F . f is Relation-like Function-like V137() V138() V139() set
rng F is functional non empty complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (Tdisk ((0. (TOP-REAL n)),1)))
N is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
FR . N is Relation-like Function-like V137() V138() V139() set
dom ((mlt ((- 1),(TOP-REAL n))) | (Tdisk ((0. (TOP-REAL n)),1))) is functional non empty complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (Tdisk ((0. (TOP-REAL n)),1)))
((mlt ((- 1),(TOP-REAL n))) | (Tdisk ((0. (TOP-REAL n)),1))) . N is Relation-like Function-like V137() V138() V139() set
(mlt ((- 1),(TOP-REAL n))) . N is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
(- 1) * N is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K368(N,(- 1)) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
- N is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
K364(N) is Relation-like NAT -defined REAL -valued Function-like V76() V137() V138() V139() M7( REAL )
|.N.| is V21() real ext-real non negative Element of REAL
n is V21() ordinal natural real V32() cardinal ext-real non negative set
TOP-REAL n is non empty V90() V91() V160() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V188() TopSpace-like T_0 T_1 T_2 strict add-continuous Mult-continuous V310() V311() finite-dimensional RLTopStruct
the carrier of (TOP-REAL n) is functional non empty complex-functions-membered ext-real-functions-membered real-functions-membered set
K19( the carrier of (TOP-REAL n)) is non empty set
0. (TOP-REAL n) is Relation-like Function-like n -element V48( TOP-REAL n) V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
the ZeroF of (TOP-REAL n) is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n)
cl_Ball ((0. (TOP-REAL n)),1) is functional non empty convex closed complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
{ b₁ where b₁ is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n) : |.(b₁ - (0. (TOP-REAL n))).| <= 1 } is set
Sphere ((0. (TOP-REAL n)),1) is functional closed complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
{ b₁ where b₁ is Relation-like Function-like n -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL n) : |.(b₁ - (0. (TOP-REAL n))).| = 1 } is set
(TOP-REAL n) | (cl_Ball ((0. (TOP-REAL n)),1)) is non empty strict TopSpace-like T_0 T_1 T_2 V310() V311() SubSpace of TOP-REAL n
[#] ((TOP-REAL n) | (cl_Ball ((0. (TOP-REAL n)),1))) is functional non empty non proper open closed dense non boundary complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of ((TOP-REAL n) | (cl_Ball ((0. (TOP-REAL n)),1))))
the carrier of ((TOP-REAL n) | (cl_Ball ((0. (TOP-REAL n)),1))) is functional non empty complex-functions-membered ext-real-functions-membered real-functions-membered set
K19( the carrier of ((TOP-REAL n) | (cl_Ball ((0. (TOP-REAL n)),1)))) is non empty set
(TOP-REAL n) | (Sphere ((0. (TOP-REAL n)),1)) is strict TopSpace-like T_0 T_1 T_2 V310() V311() SubSpace of TOP-REAL n
s is functional complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of ((TOP-REAL n) | (cl_Ball ((0. (TOP-REAL n)),1))))
((TOP-REAL n) | (cl_Ball ((0. (TOP-REAL n)),1))) | s is strict TopSpace-like T_0 T_1 T_2 V310() V311() SubSpace of (TOP-REAL n) | (cl_Ball ((0. (TOP-REAL n)),1))
A is functional non empty convex complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
(TOP-REAL n) | A is non empty strict TopSpace-like T_0 T_1 T_2 V310() V311() SubSpace of TOP-REAL n
Fr A is functional closed complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
[#] ((TOP-REAL n) | A) is functional non empty non proper open closed dense non boundary complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of ((TOP-REAL n) | A))
the carrier of ((TOP-REAL n) | A) is functional non empty complex-functions-membered ext-real-functions-membered real-functions-membered set
K19( the carrier of ((TOP-REAL n) | A)) is non empty set
FR is non empty TopSpace-like T_0 T_1 T_2 V310() V311() SubSpace of (TOP-REAL n) | A
[#] FR is functional non empty non proper open closed dense non boundary complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of FR)
the carrier of FR is functional non empty complex-functions-membered ext-real-functions-membered real-functions-membered set
K19( the carrier of FR) is non empty set
{(0. (TOP-REAL n))} is functional non empty V12() V32() 1 -element closed compact complex-functions-membered ext-real-functions-membered real-functions-membered affinely-independent Element of K19( the carrier of (TOP-REAL n))
[#] (TOP-REAL n) is functional non empty non proper non proper convex open open closed closed dense dense non boundary non boundary complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
Cl A is functional convex closed complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
(Cl A) \ A is functional complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
K20( the carrier of ((TOP-REAL n) | A), the carrier of FR) is Relation-like non empty set
K19(K20( the carrier of ((TOP-REAL n) | A), the carrier of FR)) is non empty set
F is Relation-like the carrier of ((TOP-REAL n) | A) -defined the carrier of FR -valued Function-like non empty V14( the carrier of ((TOP-REAL n) | A)) quasi_total continuous Function-yielding V275() complex-functions-valued ext-real-functions-valued real-functions-valued Element of K19(K20( the carrier of ((TOP-REAL n) | A), the carrier of FR))
K20( the carrier of ((TOP-REAL n) | A), the carrier of ((TOP-REAL n) | A)) is Relation-like non empty set
K19(K20( the carrier of ((TOP-REAL n) | A), the carrier of ((TOP-REAL n) | A))) is non empty set
f is Relation-like the carrier of ((TOP-REAL n) | A) -defined the carrier of ((TOP-REAL n) | A) -valued Function-like non empty V14( the carrier of ((TOP-REAL n) | A)) quasi_total Function-yielding V275() complex-functions-valued ext-real-functions-valued real-functions-valued Element of K19(K20( the carrier of ((TOP-REAL n) | A), the carrier of ((TOP-REAL n) | A)))
rng F is functional non empty complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of FR)
N is V21() ordinal natural real V30() V31() V32() cardinal ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered Element of NAT
TOP-REAL N is non empty V90() V91() V160() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V188() TopSpace-like T_0 T_1 T_2 strict add-continuous Mult-continuous V310() V311() finite-dimensional RLTopStruct
[#] ((TOP-REAL n) | (Sphere ((0. (TOP-REAL n)),1))) is functional non proper open closed dense complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of ((TOP-REAL n) | (Sphere ((0. (TOP-REAL n)),1))))
the carrier of ((TOP-REAL n) | (Sphere ((0. (TOP-REAL n)),1))) is functional complex-functions-membered ext-real-functions-membered real-functions-membered set
K19( the carrier of ((TOP-REAL n) | (Sphere ((0. (TOP-REAL n)),1)))) is non empty set
0. (TOP-REAL N) is Relation-like Function-like N -element V48( TOP-REAL N) V76() V137() V138() V139() Element of the carrier of (TOP-REAL N)
the carrier of (TOP-REAL N) is functional non empty complex-functions-membered ext-real-functions-membered real-functions-membered set
the ZeroF of (TOP-REAL N) is Relation-like Function-like N -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL N)
Tdisk ((0. (TOP-REAL N)),1) is non empty TopSpace-like T_0 T_1 T_2 V307(N) V310() V311() SubSpace of TOP-REAL N
cl_Ball ((0. (TOP-REAL N)),1) is functional non empty convex closed bounded compact complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL N))
K19( the carrier of (TOP-REAL N)) is non empty set
{ b₁ where b₁ is Relation-like Function-like N -element V76() V137() V138() V139() Element of the carrier of (TOP-REAL N) : |.(b₁ - (0. (TOP-REAL N))).| <= 1 } is set
(TOP-REAL N) | (cl_Ball ((0. (TOP-REAL N)),1)) is non empty strict TopSpace-like T_0 T_1 T_2 compact V310() V311() SubSpace of TOP-REAL N
Tcircle ((0. (TOP-REAL N)),1) is TopSpace-like T_0 T_1 T_2 V310() V311() SubSpace of TOP-REAL N
Ts is non empty TopSpace-like T_0 T_1 T_2 V310() V311() SubSpace of (TOP-REAL n) | (cl_Ball ((0. (TOP-REAL n)),1))
K20( the carrier of ((TOP-REAL n) | (cl_Ball ((0. (TOP-REAL n)),1))), the carrier of ((TOP-REAL n) | A)) is Relation-like non empty set
K19(K20( the carrier of ((TOP-REAL n) | (cl_Ball ((0. (TOP-REAL n)),1))), the carrier of ((TOP-REAL n) | A))) is non empty set
Fr (cl_Ball ((0. (TOP-REAL n)),1)) is functional closed boundary nowhere_dense complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of (TOP-REAL n))
h is Relation-like the carrier of ((TOP-REAL n) | (cl_Ball ((0. (TOP-REAL n)),1))) -defined the carrier of ((TOP-REAL n) | A) -valued Function-like non empty V14( the carrier of ((TOP-REAL n) | (cl_Ball ((0. (TOP-REAL n)),1)))) quasi_total Function-yielding V275() complex-functions-valued ext-real-functions-valued real-functions-valued Element of K19(K20( the carrier of ((TOP-REAL n) | (cl_Ball ((0. (TOP-REAL n)),1))), the carrier of ((TOP-REAL n) | A)))
h .: (Fr (cl_Ball ((0. (TOP-REAL n)),1))) is functional complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of ((TOP-REAL n) | A))
dom h is functional non empty complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of ((TOP-REAL n) | (cl_Ball ((0. (TOP-REAL n)),1))))
h /" is Relation-like the carrier of ((TOP-REAL n) | A) -defined the carrier of ((TOP-REAL n) | (cl_Ball ((0. (TOP-REAL n)),1))) -valued Function-like non empty V14( the carrier of ((TOP-REAL n) | A)) quasi_total Function-yielding V275() complex-functions-valued ext-real-functions-valued real-functions-valued Element of K19(K20( the carrier of ((TOP-REAL n) | A), the carrier of ((TOP-REAL n) | (cl_Ball ((0. (TOP-REAL n)),1)))))
K20( the carrier of ((TOP-REAL n) | A), the carrier of ((TOP-REAL n) | (cl_Ball ((0. (TOP-REAL n)),1)))) is Relation-like non empty set
K19(K20( the carrier of ((TOP-REAL n) | A), the carrier of ((TOP-REAL n) | (cl_Ball ((0. (TOP-REAL n)),1))))) is non empty set
(h /") * f is Relation-like the carrier of ((TOP-REAL n) | A) -defined the carrier of ((TOP-REAL n) | (cl_Ball ((0. (TOP-REAL n)),1))) -valued Function-like non empty V14( the carrier of ((TOP-REAL n) | A)) quasi_total Function-yielding V275() complex-functions-valued ext-real-functions-valued real-functions-valued Element of K19(K20( the carrier of ((TOP-REAL n) | A), the carrier of ((TOP-REAL n) | (cl_Ball ((0. (TOP-REAL n)),1)))))
rng ((h /") * f) is functional non empty complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of ((TOP-REAL n) | (cl_Ball ((0. (TOP-REAL n)),1))))
dom ((h /") * f) is functional non empty complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of ((TOP-REAL n) | A))
((h /") * f) .: (dom ((h /") * f)) is functional non empty complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of ((TOP-REAL n) | (cl_Ball ((0. (TOP-REAL n)),1))))
dom f is functional non empty complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of ((TOP-REAL n) | A))
((h /") * f) .: (dom f) is functional non empty complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of ((TOP-REAL n) | (cl_Ball ((0. (TOP-REAL n)),1))))
rng h is functional non empty complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of ((TOP-REAL n) | A))
(h /") .: (Fr A) is functional complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of ((TOP-REAL n) | (cl_Ball ((0. (TOP-REAL n)),1))))
h " (Fr A) is functional complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of ((TOP-REAL n) | (cl_Ball ((0. (TOP-REAL n)),1))))
f .: (dom f) is functional non empty complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of ((TOP-REAL n) | A))
(h /") .: (f .: (dom f)) is functional non empty complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of ((TOP-REAL n) | (cl_Ball ((0. (TOP-REAL n)),1))))
rng f is functional non empty complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of ((TOP-REAL n) | A))
(h /") .: (rng f) is functional non empty complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of ((TOP-REAL n) | (cl_Ball ((0. (TOP-REAL n)),1))))
((h /") * f) * h is Relation-like the carrier of ((TOP-REAL n) | (cl_Ball ((0. (TOP-REAL n)),1))) -defined the carrier of ((TOP-REAL n) | (cl_Ball ((0. (TOP-REAL n)),1))) -valued Function-like non empty V14( the carrier of ((TOP-REAL n) | (cl_Ball ((0. (TOP-REAL n)),1)))) quasi_total Function-yielding V275() complex-functions-valued ext-real-functions-valued real-functions-valued Element of K19(K20( the carrier of ((TOP-REAL n) | (cl_Ball ((0. (TOP-REAL n)),1))), the carrier of ((TOP-REAL n) | (cl_Ball ((0. (TOP-REAL n)),1)))))
K20( the carrier of ((TOP-REAL n) | (cl_Ball ((0. (TOP-REAL n)),1))), the carrier of ((TOP-REAL n) | (cl_Ball ((0. (TOP-REAL n)),1)))) is Relation-like non empty set
K19(K20( the carrier of ((TOP-REAL n) | (cl_Ball ((0. (TOP-REAL n)),1))), the carrier of ((TOP-REAL n) | (cl_Ball ((0. (TOP-REAL n)),1))))) is non empty set
rng (((h /") * f) * h) is functional non empty complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of ((TOP-REAL n) | (cl_Ball ((0. (TOP-REAL n)),1))))
the carrier of Ts is functional non empty complex-functions-membered ext-real-functions-membered real-functions-membered set
K20( the carrier of ((TOP-REAL n) | (cl_Ball ((0. (TOP-REAL n)),1))), the carrier of Ts) is Relation-like non empty set
K19(K20( the carrier of ((TOP-REAL n) | (cl_Ball ((0. (TOP-REAL n)),1))), the carrier of Ts)) is non empty set
hfh is Relation-like the carrier of ((TOP-REAL n) | (cl_Ball ((0. (TOP-REAL n)),1))) -defined the carrier of Ts -valued Function-like non empty V14( the carrier of ((TOP-REAL n) | (cl_Ball ((0. (TOP-REAL n)),1)))) quasi_total Function-yielding V275() complex-functions-valued ext-real-functions-valued real-functions-valued Element of K19(K20( the carrier of ((TOP-REAL n) | (cl_Ball ((0. (TOP-REAL n)),1))), the carrier of Ts))
x is Relation-like Function-like V137() V138() V139() Element of the carrier of ((TOP-REAL n) | (cl_Ball ((0. (TOP-REAL n)),1)))
hfh . x is Relation-like Function-like V137() V138() V139() Element of the carrier of Ts
h . x is Relation-like Function-like V137() V138() V139() Element of the carrier of ((TOP-REAL n) | A)
dom hfh is functional non empty complex-functions-membered ext-real-functions-membered real-functions-membered Element of K19( the carrier of ((TOP-REAL n) | (cl_Ball ((0. (TOP-REAL n)),1))))
((h /") * f) . (h . x) is Relation-like Function-like V137() V138() V139() Element of the carrier of ((TOP-REAL n) | (cl_Ball ((0. (TOP-REAL n)),1)))
f . (h . x) is Relation-like Function-like V137() V138() V139() Element of the carrier of ((TOP-REAL n) | A)
(h /") . (f . (h . x)) is Relation-like Function-like V137() V138() V139() Element of the carrier of ((TOP-REAL n) | (cl_Ball ((0. (TOP-REAL n)),1)))
H is Relation-like Function-like set
H " is Relation-like Function-like set
(H ") . (h . x) is set