for n, i being ( ( ) ( V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) )
for q being ( ( ) ( Relation-like NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) -defined REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) -valued Function-like complex-yielding V37() V38() finite V55(b₁ : ( ( ) ( V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) ) FinSequence-like FinSubsequence-like ) Element of REAL n : ( ( ) ( V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) : ( ( ) ( non empty functional FinSequence-membered ) FinSequenceSet of REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) )
for p being ( ( ) ( Relation-like NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) -defined REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) -valued Function-like complex-yielding V37() V38() finite V55(b₁ : ( ( ) ( V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) ) FinSequence-like FinSubsequence-like ) Point of ( ( ) ( non empty ) set ) ) st i : ( ( ) ( V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) in Seg n : ( ( ) ( V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) : ( ( ) ( finite V55(b₁ : ( ( ) ( V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) ) complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded ) Element of K10(NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) : ( ( ) ( non finite ) set ) ) & q : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) -defined REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) -valued Function-like complex-yielding V37() V38() finite V55(b₁ : ( ( ) ( V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) ) FinSequence-like FinSubsequence-like ) Element of REAL b₁ : ( ( ) ( V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) : ( ( ) ( non empty functional FinSequence-membered ) FinSequenceSet of REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) ) = p : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) -defined REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) -valued Function-like complex-yielding V37() V38() finite V55(b₁ : ( ( ) ( V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) ) FinSequence-like FinSubsequence-like ) Point of ( ( ) ( non empty ) set ) ) holds
abs (p : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) -defined REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) -valued Function-like complex-yielding V37() V38() finite V55(b₁ : ( ( ) ( V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) ) FinSequence-like FinSubsequence-like ) Point of ( ( ) ( non empty ) set ) ) /. i : ( ( ) ( V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) ) : ( ( ) ( V19() real ext-real ) Element of REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( V19() real ext-real ) Element of REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) <= |.q : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) -defined REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) -valued Function-like complex-yielding V37() V38() finite V55(b₁ : ( ( ) ( V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) ) FinSequence-like FinSubsequence-like ) Element of REAL b₁ : ( ( ) ( V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) : ( ( ) ( non empty functional FinSequence-membered ) FinSequenceSet of REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) ) .| : ( ( ) ( V19() real ext-real non negative ) Element of REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) ;

for x being ( ( ) ( V19() real ext-real ) Real)
for vx being ( ( ) ( ) Element of ( ( ) ( non empty V2() ) set ) ) st vx : ( ( ) ( ) Element of ( ( ) ( non empty V2() ) set ) ) = <*x : ( ( ) ( V19() real ext-real ) Real) *> : ( ( ) ( non empty V2() Relation-like NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) -defined REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) -valued Function-like one-to-one constant complex-yielding V37() V38() V40() V41() V42() V43() finite V55(1 : ( ( ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) ) FinSequence-like FinSubsequence-like ) FinSequence of REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) holds
||.vx : ( ( ) ( ) Element of ( ( ) ( non empty V2() ) set ) ) .|| : ( ( ) ( V19() real ext-real ) Element of REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) = abs x : ( ( ) ( V19() real ext-real ) Real) : ( ( ) ( V19() real ext-real ) Element of REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) ;

for n being ( ( non empty ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) )
for x being ( ( ) ( ) Point of ( ( ) ( non empty V2() ) set ) )
for i being ( ( ) ( V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) st 1 : ( ( ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) <= i : ( ( ) ( V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) & i : ( ( ) ( V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) <= n : ( ( non empty ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) holds
||.((Proj (i : ( ( ) ( V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) ,n : ( ( non empty ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) )) : ( ( Function-like V32( the carrier of (REAL-NS b₁ : ( ( non empty ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) ) : ( ( non empty V181() ) ( non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() ) L16()) : ( ( ) ( non empty V2() ) set ) , the carrier of (REAL-NS 1 : ( ( ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) ) : ( ( non empty V181() ) ( non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() ) L16()) : ( ( ) ( non empty V2() ) set ) ) ) ( Relation-like the carrier of (REAL-NS b₁ : ( ( non empty ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) ) : ( ( non empty V181() ) ( non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() ) L16()) : ( ( ) ( non empty V2() ) set ) -defined the carrier of (REAL-NS 1 : ( ( ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) ) : ( ( non empty V181() ) ( non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() ) L16()) : ( ( ) ( non empty V2() ) set ) -valued Function-like V32( the carrier of (REAL-NS b₁ : ( ( non empty ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) ) : ( ( non empty V181() ) ( non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() ) L16()) : ( ( ) ( non empty V2() ) set ) , the carrier of (REAL-NS 1 : ( ( ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) ) : ( ( non empty V181() ) ( non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() ) L16()) : ( ( ) ( non empty V2() ) set ) ) ) Element of K10(K11( the carrier of (REAL-NS b₁ : ( ( non empty ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) ) : ( ( non empty V181() ) ( non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() ) L16()) : ( ( ) ( non empty V2() ) set ) , the carrier of (REAL-NS 1 : ( ( ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) ) : ( ( non empty V181() ) ( non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() ) L16()) : ( ( ) ( non empty V2() ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) . x : ( ( ) ( ) Point of ( ( ) ( non empty V2() ) set ) ) ) : ( ( ) ( ) Element of the carrier of (REAL-NS 1 : ( ( ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) ) : ( ( non empty V181() ) ( non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() ) L16()) : ( ( ) ( non empty V2() ) set ) ) .|| : ( ( ) ( V19() real ext-real ) Element of REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) <= ||.x : ( ( ) ( ) Point of ( ( ) ( non empty V2() ) set ) ) .|| : ( ( ) ( V19() real ext-real ) Element of REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) ;

for n being ( ( non empty ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) )
for x being ( ( ) ( ) Element of ( ( ) ( non empty V2() ) set ) )
for i being ( ( ) ( V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) holds ||.((Proj (i : ( ( ) ( V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) ,n : ( ( non empty ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) )) : ( ( Function-like V32( the carrier of (REAL-NS b₁ : ( ( non empty ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) ) : ( ( non empty V181() ) ( non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() ) L16()) : ( ( ) ( non empty V2() ) set ) , the carrier of (REAL-NS 1 : ( ( ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) ) : ( ( non empty V181() ) ( non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() ) L16()) : ( ( ) ( non empty V2() ) set ) ) ) ( Relation-like the carrier of (REAL-NS b₁ : ( ( non empty ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) ) : ( ( non empty V181() ) ( non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() ) L16()) : ( ( ) ( non empty V2() ) set ) -defined the carrier of (REAL-NS 1 : ( ( ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) ) : ( ( non empty V181() ) ( non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() ) L16()) : ( ( ) ( non empty V2() ) set ) -valued Function-like V32( the carrier of (REAL-NS b₁ : ( ( non empty ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) ) : ( ( non empty V181() ) ( non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() ) L16()) : ( ( ) ( non empty V2() ) set ) , the carrier of (REAL-NS 1 : ( ( ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) ) : ( ( non empty V181() ) ( non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() ) L16()) : ( ( ) ( non empty V2() ) set ) ) ) Element of K10(K11( the carrier of (REAL-NS b₁ : ( ( non empty ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) ) : ( ( non empty V181() ) ( non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() ) L16()) : ( ( ) ( non empty V2() ) set ) , the carrier of (REAL-NS 1 : ( ( ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) ) : ( ( non empty V181() ) ( non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() ) L16()) : ( ( ) ( non empty V2() ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) . x : ( ( ) ( ) Element of ( ( ) ( non empty V2() ) set ) ) ) : ( ( ) ( ) Element of the carrier of (REAL-NS 1 : ( ( ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) ) : ( ( non empty V181() ) ( non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() ) L16()) : ( ( ) ( non empty V2() ) set ) ) .|| : ( ( ) ( V19() real ext-real ) Element of REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) = |.((proj (i : ( ( ) ( V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) ,n : ( ( non empty ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) )) : ( ( Function-like V32( REAL b₁ : ( ( non empty ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) : ( ( ) ( non empty functional FinSequence-membered ) FinSequenceSet of REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) , REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) ) ( Relation-like REAL b₁ : ( ( non empty ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) : ( ( ) ( non empty functional FinSequence-membered ) FinSequenceSet of REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) -defined REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) -valued Function-like V32( REAL b₁ : ( ( non empty ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) : ( ( ) ( non empty functional FinSequence-membered ) FinSequenceSet of REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) , REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) complex-yielding V37() V38() ) Element of K10(K11((REAL b₁ : ( ( non empty ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) ) : ( ( ) ( non empty functional FinSequence-membered ) FinSequenceSet of REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) ,REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( complex-yielding V37() V38() non finite ) set ) ) : ( ( ) ( non finite ) set ) ) . x : ( ( ) ( ) Element of ( ( ) ( non empty V2() ) set ) ) ) : ( ( ) ( V19() real ext-real ) Element of REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) .| : ( ( ) ( V19() real ext-real ) Element of REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) ;

for n being ( ( non empty ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) )
for x being ( ( ) ( Relation-like NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) -defined REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) -valued Function-like complex-yielding V37() V38() finite V55(b₁ : ( ( non empty ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) ) FinSequence-like FinSubsequence-like ) Element of REAL n : ( ( non empty ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) : ( ( ) ( non empty functional FinSequence-membered ) FinSequenceSet of REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) )
for i being ( ( ) ( V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) st 1 : ( ( ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) <= i : ( ( ) ( V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) & i : ( ( ) ( V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) <= n : ( ( non empty ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) holds
|.((proj (i : ( ( ) ( V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) ,n : ( ( non empty ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) )) : ( ( Function-like V32( REAL b₁ : ( ( non empty ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) : ( ( ) ( non empty functional FinSequence-membered ) FinSequenceSet of REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) , REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) ) ( Relation-like REAL b₁ : ( ( non empty ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) : ( ( ) ( non empty functional FinSequence-membered ) FinSequenceSet of REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) -defined REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) -valued Function-like V32( REAL b₁ : ( ( non empty ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) : ( ( ) ( non empty functional FinSequence-membered ) FinSequenceSet of REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) , REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) complex-yielding V37() V38() ) Element of K10(K11((REAL b₁ : ( ( non empty ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) ) : ( ( ) ( non empty functional FinSequence-membered ) FinSequenceSet of REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) ,REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( complex-yielding V37() V38() non finite ) set ) ) : ( ( ) ( non finite ) set ) ) . x : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) -defined REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) -valued Function-like complex-yielding V37() V38() finite V55(b₁ : ( ( non empty ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) ) FinSequence-like FinSubsequence-like ) Element of REAL b₁ : ( ( non empty ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) : ( ( ) ( non empty functional FinSequence-membered ) FinSequenceSet of REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) ) ) : ( ( ) ( V19() real ext-real ) Element of REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) .| : ( ( ) ( V19() real ext-real ) Element of REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) <= |.x : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) -defined REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) -valued Function-like complex-yielding V37() V38() finite V55(b₁ : ( ( non empty ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) ) FinSequence-like FinSubsequence-like ) Element of REAL b₁ : ( ( non empty ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) : ( ( ) ( non empty functional FinSequence-membered ) FinSequenceSet of REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) ) .| : ( ( ) ( V19() real ext-real non negative ) Element of REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) ;

for m, n being ( ( non empty ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) )
for s being ( ( ) ( Relation-like Function-like ) Point of ( ( ) ( non empty ) set ) )
for i being ( ( ) ( V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) st 1 : ( ( ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) <= i : ( ( ) ( V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) & i : ( ( ) ( V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) <= n : ( ( non empty ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) holds
( Proj (i : ( ( ) ( V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) ,n : ( ( non empty ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) ) : ( ( Function-like V32( the carrier of (REAL-NS b₂ : ( ( non empty ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) ) : ( ( non empty V181() ) ( non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() ) L16()) : ( ( ) ( non empty V2() ) set ) , the carrier of (REAL-NS 1 : ( ( ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) ) : ( ( non empty V181() ) ( non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() ) L16()) : ( ( ) ( non empty V2() ) set ) ) ) ( Relation-like the carrier of (REAL-NS b₂ : ( ( non empty ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) ) : ( ( non empty V181() ) ( non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() ) L16()) : ( ( ) ( non empty V2() ) set ) -defined the carrier of (REAL-NS 1 : ( ( ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) ) : ( ( non empty V181() ) ( non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() ) L16()) : ( ( ) ( non empty V2() ) set ) -valued Function-like V32( the carrier of (REAL-NS b₂ : ( ( non empty ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) ) : ( ( non empty V181() ) ( non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() ) L16()) : ( ( ) ( non empty V2() ) set ) , the carrier of (REAL-NS 1 : ( ( ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) ) : ( ( non empty V181() ) ( non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() ) L16()) : ( ( ) ( non empty V2() ) set ) ) ) Element of K10(K11( the carrier of (REAL-NS b₂ : ( ( non empty ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) ) : ( ( non empty V181() ) ( non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() ) L16()) : ( ( ) ( non empty V2() ) set ) , the carrier of (REAL-NS 1 : ( ( ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) ) : ( ( non empty V181() ) ( non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() ) L16()) : ( ( ) ( non empty V2() ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) is ( ( Function-like V32( the carrier of (REAL-NS b₂ : ( ( non empty ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) ) : ( ( non empty V181() ) ( non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() ) L16()) : ( ( ) ( non empty V2() ) set ) , the carrier of (REAL-NS 1 : ( ( ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) ) : ( ( non empty V181() ) ( non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() ) L16()) : ( ( ) ( non empty V2() ) set ) ) V149( REAL-NS b₂ : ( ( non empty ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) : ( ( non empty V181() ) ( non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() ) L16()) , REAL-NS 1 : ( ( ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) : ( ( non empty V181() ) ( non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() ) L16()) ) homogeneous Lipschitzian ) ( Relation-like the carrier of (REAL-NS b₂ : ( ( non empty ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) ) : ( ( non empty V181() ) ( non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() ) L16()) : ( ( ) ( non empty V2() ) set ) -defined the carrier of (REAL-NS 1 : ( ( ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) ) : ( ( non empty V181() ) ( non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() ) L16()) : ( ( ) ( non empty V2() ) set ) -valued Function-like V32( the carrier of (REAL-NS b₂ : ( ( non empty ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) ) : ( ( non empty V181() ) ( non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() ) L16()) : ( ( ) ( non empty V2() ) set ) , the carrier of (REAL-NS 1 : ( ( ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) ) : ( ( non empty V181() ) ( non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() ) L16()) : ( ( ) ( non empty V2() ) set ) ) V149( REAL-NS b₂ : ( ( non empty ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) : ( ( non empty V181() ) ( non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() ) L16()) , REAL-NS 1 : ( ( ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) : ( ( non empty V181() ) ( non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() ) L16()) ) homogeneous Lipschitzian ) LinearOperator of REAL-NS n : ( ( non empty ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) : ( ( non empty V181() ) ( non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() ) L16()) , REAL-NS 1 : ( ( ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) : ( ( non empty V181() ) ( non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() ) L16()) ) & (BoundedLinearOperatorsNorm ((REAL-NS n : ( ( non empty ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) ) : ( ( non empty V181() ) ( non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() ) L16()) ,(REAL-NS 1 : ( ( ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) ) : ( ( non empty V181() ) ( non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() ) L16()) )) : ( ( Function-like V32( BoundedLinearOperators ((REAL-NS b₂ : ( ( non empty ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) ) : ( ( non empty V181() ) ( non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() ) L16()) ,(REAL-NS 1 : ( ( ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) ) : ( ( non empty V181() ) ( non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() ) L16()) ) : ( ( ) ( non empty ) Element of K10( the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS b₂ : ( ( non empty ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) ) : ( ( non empty V181() ) ( non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() ) L16()) ,(REAL-NS 1 : ( ( ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) ) : ( ( non empty V181() ) ( non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() ) L16()) )) : ( ( non empty V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty V107() V151() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) RLSStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) ) ( Relation-like BoundedLinearOperators ((REAL-NS b₂ : ( ( non empty ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) ) : ( ( non empty V181() ) ( non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() ) L16()) ,(REAL-NS 1 : ( ( ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) ) : ( ( non empty V181() ) ( non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() ) L16()) ) : ( ( ) ( non empty ) Element of K10( the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS b₂ : ( ( non empty ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) ) : ( ( non empty V181() ) ( non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() ) L16()) ,(REAL-NS 1 : ( ( ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) ) : ( ( non empty V181() ) ( non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() ) L16()) )) : ( ( non empty V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty V107() V151() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) RLSStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) -defined REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) -valued Function-like V32( BoundedLinearOperators ((REAL-NS b₂ : ( ( non empty ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) ) : ( ( non empty V181() ) ( non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() ) L16()) ,(REAL-NS 1 : ( ( ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) ) : ( ( non empty V181() ) ( non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() ) L16()) ) : ( ( ) ( non empty ) Element of K10( the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS b₂ : ( ( non empty ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) ) : ( ( non empty V181() ) ( non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() ) L16()) ,(REAL-NS 1 : ( ( ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) ) : ( ( non empty V181() ) ( non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() ) L16()) )) : ( ( non empty V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty V107() V151() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) RLSStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) complex-yielding V37() V38() ) Element of K10(K11((BoundedLinearOperators ((REAL-NS b₂ : ( ( non empty ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) ) : ( ( non empty V181() ) ( non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() ) L16()) ,(REAL-NS 1 : ( ( ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) ) : ( ( non empty V181() ) ( non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() ) L16()) )) : ( ( ) ( non empty ) Element of K10( the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS b₂ : ( ( non empty ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) ) : ( ( non empty V181() ) ( non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() ) L16()) ,(REAL-NS 1 : ( ( ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) ) : ( ( non empty V181() ) ( non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() ) L16()) )) : ( ( non empty V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) ( non empty V107() V151() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ) RLSStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ,REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( complex-yielding V37() V38() non finite ) set ) ) : ( ( ) ( non finite ) set ) ) . (Proj (i : ( ( ) ( V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) ,n : ( ( non empty ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) )) : ( ( Function-like V32( the carrier of (REAL-NS b₂ : ( ( non empty ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) ) : ( ( non empty V181() ) ( non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() ) L16()) : ( ( ) ( non empty V2() ) set ) , the carrier of (REAL-NS 1 : ( ( ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) ) : ( ( non empty V181() ) ( non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() ) L16()) : ( ( ) ( non empty V2() ) set ) ) ) ( Relation-like the carrier of (REAL-NS b₂ : ( ( non empty ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) ) : ( ( non empty V181() ) ( non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() ) L16()) : ( ( ) ( non empty V2() ) set ) -defined the carrier of (REAL-NS 1 : ( ( ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) ) : ( ( non empty V181() ) ( non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() ) L16()) : ( ( ) ( non empty V2() ) set ) -valued Function-like V32( the carrier of (REAL-NS b₂ : ( ( non empty ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) ) : ( ( non empty V181() ) ( non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() ) L16()) : ( ( ) ( non empty V2() ) set ) , the carrier of (REAL-NS 1 : ( ( ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) ) : ( ( non empty V181() ) ( non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() ) L16()) : ( ( ) ( non empty V2() ) set ) ) ) Element of K10(K11( the carrier of (REAL-NS b₂ : ( ( non empty ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) ) : ( ( non empty V181() ) ( non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() ) L16()) : ( ( ) ( non empty V2() ) set ) , the carrier of (REAL-NS 1 : ( ( ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) ) : ( ( non empty V181() ) ( non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() ) L16()) : ( ( ) ( non empty V2() ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( V19() real ext-real ) Element of REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) <= 1 : ( ( ) ( non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded ) Element of NAT : ( ( ) ( non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below ) Element of K10(REAL : ( ( ) ( non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() ) set ) ) : ( ( ) ( non finite ) set ) ) ) ) ;