:: NCFCONT1 semantic presentation

REAL is non empty V45() V46() V47() V51() V52() set
NAT is non empty epsilon-transitive epsilon-connected ordinal V45() V46() V47() V48() V49() V50() V51() Element of K6(REAL)
K6(REAL) is set
COMPLEX is non empty V45() V51() V52() set
RAT is non empty V45() V46() V47() V48() V51() V52() set
INT is non empty V45() V46() V47() V48() V49() V51() V52() set
omega is non empty epsilon-transitive epsilon-connected ordinal V45() V46() V47() V48() V49() V50() V51() set
K6(omega) is set
K6(NAT) is set
K7(COMPLEX,COMPLEX) is complex-valued set
K6(K7(COMPLEX,COMPLEX)) is set
K7(COMPLEX,REAL) is complex-valued ext-real-valued real-valued set
K6(K7(COMPLEX,REAL)) is set
K7(NAT,REAL) is complex-valued ext-real-valued real-valued set
K6(K7(NAT,REAL)) is set
K7(NAT,COMPLEX) is complex-valued set
K6(K7(NAT,COMPLEX)) is set
{} is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() real ext-real non negative V45() V46() V47() V48() V49() V50() V51() set
1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
0 is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() V51() Element of NAT
- 1 is V11() real ext-real non positive Element of REAL
1r is V11() Element of COMPLEX
- 1r is V11() Element of COMPLEX
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
K7(NAT, the carrier of CNS) is set
K6(K7(NAT, the carrier of CNS)) is set
X is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
- X is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
(- 1r) * X is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
f is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
((- 1r) * X) . f is Element of the carrier of CNS
X . f is Element of the carrier of CNS
(- 1r) * (X . f) is Element of the carrier of CNS
- (X . f) is Element of the carrier of CNS
(- X) . f is Element of the carrier of CNS
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
K6( the carrier of CNS) is set
X is Element of the carrier of CNS
{ b₁ where b₁ is Element of the carrier of CNS : not 1 <= ||.(b₁ - X).|| } is set
x0 is set
p is Element of the carrier of CNS
p - X is Element of the carrier of CNS
||.(p - X).|| is V11() real ext-real Element of REAL
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is Element of the carrier of CNS
f is V11() real ext-real Element of REAL
{ b₁ where b₁ is Element of the carrier of CNS : not f <= ||.(b₁ - X).|| } is set
p is set
x1 is Element of the carrier of CNS
x1 - X is Element of the carrier of CNS
||.(x1 - X).|| is V11() real ext-real Element of REAL
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is Element of the carrier of CNS
f is (CNS,X)
x0 is V11() real ext-real Element of REAL
{ b₁ where b₁ is Element of the carrier of CNS : not x0 <= ||.(b₁ - X).|| } is set
X - X is Element of the carrier of CNS
||.(X - X).|| is V11() real ext-real Element of REAL
0. CNS is V97(CNS) Element of the carrier of CNS
||.(0. CNS).|| is V11() real ext-real Element of REAL
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
K6( the carrier of CNS) is set
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
K6( the carrier of CNS) is set
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
K6( the carrier of CNS) is set
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of X is non empty set
K7( the carrier of CNS, the carrier of X) is set
K6(K7( the carrier of CNS, the carrier of X)) is set
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of X is non empty set
K7( the carrier of CNS, the carrier of X) is set
K6(K7( the carrier of CNS, the carrier of X)) is set
CNS is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of X is non empty set
K7( the carrier of CNS, the carrier of X) is set
K6(K7( the carrier of CNS, the carrier of X)) is set
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
K7( the carrier of CNS,COMPLEX) is complex-valued set
K6(K7( the carrier of CNS,COMPLEX)) is set
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
K7( the carrier of CNS,REAL) is complex-valued ext-real-valued real-valued set
K6(K7( the carrier of CNS,REAL)) is set
CNS is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of CNS is non empty set
K7( the carrier of CNS,COMPLEX) is complex-valued set
K6(K7( the carrier of CNS,COMPLEX)) is set
CNS is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
X is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of X is non empty set
K7(NAT, the carrier of X) is set
K6(K7(NAT, the carrier of X)) is set
f is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of f is non empty set
K7( the carrier of X, the carrier of f) is set
K6(K7( the carrier of X, the carrier of f)) is set
x0 is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
rng x0 is Element of K6( the carrier of X)
K6( the carrier of X) is set
x0 . CNS is Element of the carrier of X
p is Relation-like the carrier of X -defined the carrier of f -valued Function-like Element of K6(K7( the carrier of X, the carrier of f))
dom p is Element of K6( the carrier of X)
dom x0 is V45() V46() V47() V48() V49() V50() Element of K6(NAT)
x0 (#) p is Relation-like set
dom (x0 (#) p) is set
CNS is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
X is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of X is non empty set
K7(NAT, the carrier of X) is set
K6(K7(NAT, the carrier of X)) is set
f is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of f is non empty set
K7( the carrier of X, the carrier of f) is set
K6(K7( the carrier of X, the carrier of f)) is set
x0 is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
rng x0 is Element of K6( the carrier of X)
K6( the carrier of X) is set
x0 . CNS is Element of the carrier of X
p is Relation-like the carrier of X -defined the carrier of f -valued Function-like Element of K6(K7( the carrier of X, the carrier of f))
dom p is Element of K6( the carrier of X)
dom x0 is V45() V46() V47() V48() V49() V50() Element of K6(NAT)
x0 (#) p is Relation-like set
dom (x0 (#) p) is set
CNS is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
X is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of X is non empty set
f is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of f is non empty set
K7(NAT, the carrier of f) is set
K6(K7(NAT, the carrier of f)) is set
K7( the carrier of f, the carrier of X) is set
K6(K7( the carrier of f, the carrier of X)) is set
x0 is non empty Relation-like NAT -defined the carrier of f -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of f))
rng x0 is Element of K6( the carrier of f)
K6( the carrier of f) is set
x0 . CNS is Element of the carrier of f
p is Relation-like the carrier of f -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of f, the carrier of X))
dom p is Element of K6( the carrier of f)
dom x0 is V45() V46() V47() V48() V49() V50() Element of K6(NAT)
x0 (#) p is Relation-like set
dom (x0 (#) p) is set
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
K7(NAT, the carrier of CNS) is set
K6(K7(NAT, the carrier of CNS)) is set
X is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
rng X is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
f is set
dom X is V45() V46() V47() V48() V49() V50() Element of K6(NAT)
x0 is set
X . x0 is set
p is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
X . p is Element of the carrier of CNS
x0 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
X . x0 is Element of the carrier of CNS
dom X is V45() V46() V47() V48() V49() V50() Element of K6(NAT)
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of X is non empty set
K7( the carrier of CNS, the carrier of X) is set
K6(K7( the carrier of CNS, the carrier of X)) is set
f is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
dom f is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
x0 is Element of the carrier of CNS
f /. x0 is Element of the carrier of X
p is V11() real ext-real Element of REAL
x1 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
x1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative Element of REAL
1 / (x1 + 1) is V11() real ext-real non negative Element of REAL
(x1 + 1) " is V11() real ext-real positive non negative Element of REAL
x2 is Element of the carrier of CNS
x2 - x0 is Element of the carrier of CNS
||.(x2 - x0).|| is V11() real ext-real Element of REAL
f /. x2 is Element of the carrier of X
(f /. x2) - (f /. x0) is Element of the carrier of X
||.((f /. x2) - (f /. x0)).|| is V11() real ext-real Element of REAL
K7(NAT, the carrier of CNS) is set
K6(K7(NAT, the carrier of CNS)) is set
x1 is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
x2 is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
rng x2 is Element of K6( the carrier of CNS)
dom x2 is V45() V46() V47() V48() V49() V50() Element of K6(NAT)
s9 is set
x1 is set
x2 . x1 is set
s9 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
x2 . s9 is Element of the carrier of CNS
f /. (x2 . s9) is Element of the carrier of X
(f /. (x2 . s9)) - (f /. x0) is Element of the carrier of X
||.((f /. (x2 . s9)) - (f /. x0)).|| is V11() real ext-real Element of REAL
f /* x2 is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
K7(NAT, the carrier of X) is set
K6(K7(NAT, the carrier of X)) is set
(f /* x2) . s9 is Element of the carrier of X
((f /* x2) . s9) - (f /. x0) is Element of the carrier of X
||.(((f /* x2) . s9) - (f /. x0)).|| is V11() real ext-real Element of REAL
s9 is V11() real ext-real Element of REAL
s9 " is V11() real ext-real Element of REAL
x1 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
x1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative Element of REAL
(s9 ") + 0 is V11() real ext-real Element of REAL
1 / (s9 ") is V11() real ext-real Element of REAL
1 / (x1 + 1) is V11() real ext-real non negative Element of REAL
x1 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
x2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
x1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative Element of REAL
x2 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative Element of REAL
1 / (x2 + 1) is V11() real ext-real non negative Element of REAL
1 / (x1 + 1) is V11() real ext-real non negative Element of REAL
x2 . x2 is Element of the carrier of CNS
(x2 . x2) - x0 is Element of the carrier of CNS
||.((x2 . x2) - x0).|| is V11() real ext-real Element of REAL
lim x2 is Element of the carrier of CNS
lim (f /* x2) is Element of the carrier of X
s9 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
(f /* x2) . s9 is Element of the carrier of X
((f /* x2) . s9) - (f /. x0) is Element of the carrier of X
||.(((f /* x2) . s9) - (f /. x0)).|| is V11() real ext-real Element of REAL
K7(NAT, the carrier of CNS) is set
K6(K7(NAT, the carrier of CNS)) is set
p is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
rng p is Element of K6( the carrier of CNS)
lim p is Element of the carrier of CNS
x1 is V11() real ext-real Element of REAL
x2 is V11() real ext-real Element of REAL
s9 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
x1 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
x1 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
p . x1 is Element of the carrier of CNS
(p . x1) - x0 is Element of the carrier of CNS
||.((p . x1) - x0).|| is V11() real ext-real Element of REAL
dom p is V45() V46() V47() V48() V49() V50() Element of K6(NAT)
f /. (p . x1) is Element of the carrier of X
(f /. (p . x1)) - (f /. x0) is Element of the carrier of X
||.((f /. (p . x1)) - (f /. x0)).|| is V11() real ext-real Element of REAL
f /* p is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
K7(NAT, the carrier of X) is set
K6(K7(NAT, the carrier of X)) is set
(f /* p) . x1 is Element of the carrier of X
((f /* p) . x1) - (f /. x0) is Element of the carrier of X
||.(((f /* p) . x1) - (f /. x0)).|| is V11() real ext-real Element of REAL
lim (f /* p) is Element of the carrier of X
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of X is non empty set
K7( the carrier of CNS, the carrier of X) is set
K6(K7( the carrier of CNS, the carrier of X)) is set
f is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
dom f is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
x0 is Element of the carrier of CNS
f /. x0 is Element of the carrier of X
p is V11() real ext-real Element of REAL
x1 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
x1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative Element of REAL
1 / (x1 + 1) is V11() real ext-real non negative Element of REAL
(x1 + 1) " is V11() real ext-real positive non negative Element of REAL
x2 is Element of the carrier of CNS
x2 - x0 is Element of the carrier of CNS
||.(x2 - x0).|| is V11() real ext-real Element of REAL
f /. x2 is Element of the carrier of X
(f /. x2) - (f /. x0) is Element of the carrier of X
||.((f /. x2) - (f /. x0)).|| is V11() real ext-real Element of REAL
K7(NAT, the carrier of CNS) is set
K6(K7(NAT, the carrier of CNS)) is set
x1 is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
x2 is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
rng x2 is Element of K6( the carrier of CNS)
dom x2 is V45() V46() V47() V48() V49() V50() Element of K6(NAT)
s9 is set
x1 is set
x2 . x1 is set
s9 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
x2 . s9 is Element of the carrier of CNS
f /. (x2 . s9) is Element of the carrier of X
(f /. (x2 . s9)) - (f /. x0) is Element of the carrier of X
||.((f /. (x2 . s9)) - (f /. x0)).|| is V11() real ext-real Element of REAL
f /* x2 is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
K7(NAT, the carrier of X) is set
K6(K7(NAT, the carrier of X)) is set
(f /* x2) . s9 is Element of the carrier of X
((f /* x2) . s9) - (f /. x0) is Element of the carrier of X
||.(((f /* x2) . s9) - (f /. x0)).|| is V11() real ext-real Element of REAL
s9 is V11() real ext-real Element of REAL
s9 " is V11() real ext-real Element of REAL
x1 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
x1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative Element of REAL
(s9 ") + 0 is V11() real ext-real Element of REAL
1 / (s9 ") is V11() real ext-real Element of REAL
1 / (x1 + 1) is V11() real ext-real non negative Element of REAL
x1 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
x2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
x1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative Element of REAL
x2 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative Element of REAL
1 / (x2 + 1) is V11() real ext-real non negative Element of REAL
1 / (x1 + 1) is V11() real ext-real non negative Element of REAL
x2 . x2 is Element of the carrier of CNS
(x2 . x2) - x0 is Element of the carrier of CNS
||.((x2 . x2) - x0).|| is V11() real ext-real Element of REAL
lim x2 is Element of the carrier of CNS
lim (f /* x2) is Element of the carrier of X
s9 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
(f /* x2) . s9 is Element of the carrier of X
((f /* x2) . s9) - (f /. x0) is Element of the carrier of X
||.(((f /* x2) . s9) - (f /. x0)).|| is V11() real ext-real Element of REAL
K7(NAT, the carrier of CNS) is set
K6(K7(NAT, the carrier of CNS)) is set
p is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
rng p is Element of K6( the carrier of CNS)
lim p is Element of the carrier of CNS
x1 is V11() real ext-real Element of REAL
x2 is V11() real ext-real Element of REAL
s9 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
x1 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
x1 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
p . x1 is Element of the carrier of CNS
(p . x1) - x0 is Element of the carrier of CNS
||.((p . x1) - x0).|| is V11() real ext-real Element of REAL
dom p is V45() V46() V47() V48() V49() V50() Element of K6(NAT)
f /. (p . x1) is Element of the carrier of X
(f /. (p . x1)) - (f /. x0) is Element of the carrier of X
||.((f /. (p . x1)) - (f /. x0)).|| is V11() real ext-real Element of REAL
f /* p is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
K7(NAT, the carrier of X) is set
K6(K7(NAT, the carrier of X)) is set
(f /* p) . x1 is Element of the carrier of X
((f /* p) . x1) - (f /. x0) is Element of the carrier of X
||.(((f /* p) . x1) - (f /. x0)).|| is V11() real ext-real Element of REAL
lim (f /* p) is Element of the carrier of X
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of X is non empty set
K7( the carrier of X, the carrier of CNS) is set
K6(K7( the carrier of X, the carrier of CNS)) is set
f is Relation-like the carrier of X -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of X, the carrier of CNS))
dom f is Element of K6( the carrier of X)
K6( the carrier of X) is set
x0 is Element of the carrier of X
f /. x0 is Element of the carrier of CNS
p is V11() real ext-real Element of REAL
x1 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
x1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative Element of REAL
1 / (x1 + 1) is V11() real ext-real non negative Element of REAL
(x1 + 1) " is V11() real ext-real positive non negative Element of REAL
x2 is Element of the carrier of X
x2 - x0 is Element of the carrier of X
||.(x2 - x0).|| is V11() real ext-real Element of REAL
f /. x2 is Element of the carrier of CNS
(f /. x2) - (f /. x0) is Element of the carrier of CNS
||.((f /. x2) - (f /. x0)).|| is V11() real ext-real Element of REAL
K7(NAT, the carrier of X) is set
K6(K7(NAT, the carrier of X)) is set
x1 is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
x2 is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
rng x2 is Element of K6( the carrier of X)
dom x2 is V45() V46() V47() V48() V49() V50() Element of K6(NAT)
s9 is set
x1 is set
x2 . x1 is set
s9 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
x2 . s9 is Element of the carrier of X
f /. (x2 . s9) is Element of the carrier of CNS
(f /. (x2 . s9)) - (f /. x0) is Element of the carrier of CNS
||.((f /. (x2 . s9)) - (f /. x0)).|| is V11() real ext-real Element of REAL
f /* x2 is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
K7(NAT, the carrier of CNS) is set
K6(K7(NAT, the carrier of CNS)) is set
(f /* x2) . s9 is Element of the carrier of CNS
((f /* x2) . s9) - (f /. x0) is Element of the carrier of CNS
||.(((f /* x2) . s9) - (f /. x0)).|| is V11() real ext-real Element of REAL
s9 is V11() real ext-real Element of REAL
s9 " is V11() real ext-real Element of REAL
x1 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
x1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative Element of REAL
(s9 ") + 0 is V11() real ext-real Element of REAL
1 / (s9 ") is V11() real ext-real Element of REAL
1 / (x1 + 1) is V11() real ext-real non negative Element of REAL
x1 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
x2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
x1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative Element of REAL
x2 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative Element of REAL
1 / (x2 + 1) is V11() real ext-real non negative Element of REAL
1 / (x1 + 1) is V11() real ext-real non negative Element of REAL
x2 . x2 is Element of the carrier of X
(x2 . x2) - x0 is Element of the carrier of X
||.((x2 . x2) - x0).|| is V11() real ext-real Element of REAL
lim x2 is Element of the carrier of X
lim (f /* x2) is Element of the carrier of CNS
s9 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
(f /* x2) . s9 is Element of the carrier of CNS
((f /* x2) . s9) - (f /. x0) is Element of the carrier of CNS
||.(((f /* x2) . s9) - (f /. x0)).|| is V11() real ext-real Element of REAL
K7(NAT, the carrier of X) is set
K6(K7(NAT, the carrier of X)) is set
p is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
rng p is Element of K6( the carrier of X)
lim p is Element of the carrier of X
x1 is V11() real ext-real Element of REAL
x2 is V11() real ext-real Element of REAL
s9 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
x1 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
x1 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
p . x1 is Element of the carrier of X
(p . x1) - x0 is Element of the carrier of X
||.((p . x1) - x0).|| is V11() real ext-real Element of REAL
dom p is V45() V46() V47() V48() V49() V50() Element of K6(NAT)
f /. (p . x1) is Element of the carrier of CNS
(f /. (p . x1)) - (f /. x0) is Element of the carrier of CNS
||.((f /. (p . x1)) - (f /. x0)).|| is V11() real ext-real Element of REAL
f /* p is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
K7(NAT, the carrier of CNS) is set
K6(K7(NAT, the carrier of CNS)) is set
(f /* p) . x1 is Element of the carrier of CNS
((f /* p) . x1) - (f /. x0) is Element of the carrier of CNS
||.(((f /* p) . x1) - (f /. x0)).|| is V11() real ext-real Element of REAL
lim (f /* p) is Element of the carrier of CNS
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
K7( the carrier of CNS,REAL) is complex-valued ext-real-valued real-valued set
K6(K7( the carrier of CNS,REAL)) is set
X is Relation-like the carrier of CNS -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7( the carrier of CNS,REAL))
dom X is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
f is Element of the carrier of CNS
X /. f is V11() real ext-real Element of REAL
x0 is V11() real ext-real Element of REAL
p is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
p + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative Element of REAL
1 / (p + 1) is V11() real ext-real non negative Element of REAL
(p + 1) " is V11() real ext-real positive non negative Element of REAL
x1 is Element of the carrier of CNS
x1 - f is Element of the carrier of CNS
||.(x1 - f).|| is V11() real ext-real Element of REAL
X /. x1 is V11() real ext-real Element of REAL
(X /. x1) - (X /. f) is V11() real ext-real Element of REAL
abs ((X /. x1) - (X /. f)) is V11() real ext-real Element of REAL
K7(NAT, the carrier of CNS) is set
K6(K7(NAT, the carrier of CNS)) is set
p is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
x1 is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
rng x1 is Element of K6( the carrier of CNS)
dom x1 is V45() V46() V47() V48() V49() V50() Element of K6(NAT)
x2 is set
s9 is set
x1 . s9 is set
x2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
x1 . x2 is Element of the carrier of CNS
X /. (x1 . x2) is V11() real ext-real Element of REAL
(X /. (x1 . x2)) - (X /. f) is V11() real ext-real Element of REAL
abs ((X /. (x1 . x2)) - (X /. f)) is V11() real ext-real Element of REAL
X /* x1 is non empty Relation-like NAT -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(X /* x1) . x2 is V11() real ext-real Element of REAL
((X /* x1) . x2) - (X /. f) is V11() real ext-real Element of REAL
abs (((X /* x1) . x2) - (X /. f)) is V11() real ext-real Element of REAL
x2 is V11() real ext-real Element of REAL
x2 " is V11() real ext-real Element of REAL
s9 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
s9 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative Element of REAL
(x2 ") + 0 is V11() real ext-real Element of REAL
1 / (x2 ") is V11() real ext-real Element of REAL
1 / (s9 + 1) is V11() real ext-real non negative Element of REAL
x1 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
x1 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
x1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative Element of REAL
x1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative Element of REAL
1 / (x1 + 1) is V11() real ext-real non negative Element of REAL
1 / (x1 + 1) is V11() real ext-real non negative Element of REAL
x1 . x1 is Element of the carrier of CNS
(x1 . x1) - f is Element of the carrier of CNS
||.((x1 . x1) - f).|| is V11() real ext-real Element of REAL
lim x1 is Element of the carrier of CNS
lim (X /* x1) is V11() real ext-real Element of REAL
x2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
(X /* x1) . x2 is V11() real ext-real Element of REAL
((X /* x1) . x2) - (X /. f) is V11() real ext-real Element of REAL
abs (((X /* x1) . x2) - (X /. f)) is V11() real ext-real Element of REAL
K7(NAT, the carrier of CNS) is set
K6(K7(NAT, the carrier of CNS)) is set
x0 is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
rng x0 is Element of K6( the carrier of CNS)
lim x0 is Element of the carrier of CNS
p is V11() real ext-real set
x1 is V11() real ext-real Element of REAL
x2 is V11() real ext-real Element of REAL
s9 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
x1 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
x1 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
x0 . x1 is Element of the carrier of CNS
(x0 . x1) - f is Element of the carrier of CNS
||.((x0 . x1) - f).|| is V11() real ext-real Element of REAL
dom x0 is V45() V46() V47() V48() V49() V50() Element of K6(NAT)
X /. (x0 . x1) is V11() real ext-real Element of REAL
(X /. (x0 . x1)) - (X /. f) is V11() real ext-real Element of REAL
abs ((X /. (x0 . x1)) - (X /. f)) is V11() real ext-real Element of REAL
X /* x0 is non empty Relation-like NAT -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(X /* x0) . x1 is V11() real ext-real Element of REAL
((X /* x0) . x1) - (X /. f) is V11() real ext-real Element of REAL
abs (((X /* x0) . x1) - (X /. f)) is V11() real ext-real Element of REAL
lim (X /* x0) is V11() real ext-real Element of REAL
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
K7( the carrier of CNS,COMPLEX) is complex-valued set
K6(K7( the carrier of CNS,COMPLEX)) is set
X is Relation-like the carrier of CNS -defined COMPLEX -valued Function-like complex-valued Element of K6(K7( the carrier of CNS,COMPLEX))
dom X is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
f is Element of the carrier of CNS
X /. f is V11() Element of COMPLEX
x0 is V11() real ext-real Element of REAL
p is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
p + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative Element of REAL
1 / (p + 1) is V11() real ext-real non negative Element of REAL
(p + 1) " is V11() real ext-real positive non negative Element of REAL
x1 is Element of the carrier of CNS
x1 - f is Element of the carrier of CNS
||.(x1 - f).|| is V11() real ext-real Element of REAL
X /. x1 is V11() Element of COMPLEX
(X /. x1) - (X /. f) is V11() Element of COMPLEX
|.((X /. x1) - (X /. f)).| is V11() real ext-real Element of REAL
K7(NAT, the carrier of CNS) is set
K6(K7(NAT, the carrier of CNS)) is set
p is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
x1 is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
rng x1 is Element of K6( the carrier of CNS)
dom x1 is V45() V46() V47() V48() V49() V50() Element of K6(NAT)
x2 is set
s9 is set
x1 . s9 is set
x2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
x1 . x2 is Element of the carrier of CNS
X /. (x1 . x2) is V11() Element of COMPLEX
(X /. (x1 . x2)) - (X /. f) is V11() Element of COMPLEX
|.((X /. (x1 . x2)) - (X /. f)).| is V11() real ext-real Element of REAL
X /* x1 is non empty Relation-like NAT -defined COMPLEX -valued Function-like total quasi_total complex-valued Element of K6(K7(NAT,COMPLEX))
(X /* x1) . x2 is V11() Element of COMPLEX
((X /* x1) . x2) - (X /. f) is V11() Element of COMPLEX
|.(((X /* x1) . x2) - (X /. f)).| is V11() real ext-real Element of REAL
x2 is V11() real ext-real Element of REAL
x2 " is V11() real ext-real Element of REAL
s9 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
s9 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative Element of REAL
(x2 ") + 0 is V11() real ext-real Element of REAL
1 / (x2 ") is V11() real ext-real Element of REAL
1 / (s9 + 1) is V11() real ext-real non negative Element of REAL
x1 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
x1 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
x1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative Element of REAL
x1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative Element of REAL
1 / (x1 + 1) is V11() real ext-real non negative Element of REAL
1 / (x1 + 1) is V11() real ext-real non negative Element of REAL
x1 . x1 is Element of the carrier of CNS
(x1 . x1) - f is Element of the carrier of CNS
||.((x1 . x1) - f).|| is V11() real ext-real Element of REAL
lim x1 is Element of the carrier of CNS
lim (X /* x1) is V11() Element of COMPLEX
x2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
(X /* x1) . x2 is V11() Element of COMPLEX
((X /* x1) . x2) - (X /. f) is V11() Element of COMPLEX
|.(((X /* x1) . x2) - (X /. f)).| is V11() real ext-real Element of REAL
K7(NAT, the carrier of CNS) is set
K6(K7(NAT, the carrier of CNS)) is set
x0 is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
rng x0 is Element of K6( the carrier of CNS)
lim x0 is Element of the carrier of CNS
p is V11() real ext-real Element of REAL
x1 is V11() real ext-real Element of REAL
x2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
s9 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
x1 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
x0 . x1 is Element of the carrier of CNS
(x0 . x1) - f is Element of the carrier of CNS
||.((x0 . x1) - f).|| is V11() real ext-real Element of REAL
dom x0 is V45() V46() V47() V48() V49() V50() Element of K6(NAT)
X /. (x0 . x1) is V11() Element of COMPLEX
(X /. (x0 . x1)) - (X /. f) is V11() Element of COMPLEX
|.((X /. (x0 . x1)) - (X /. f)).| is V11() real ext-real Element of REAL
X /* x0 is non empty Relation-like NAT -defined COMPLEX -valued Function-like total quasi_total complex-valued Element of K6(K7(NAT,COMPLEX))
(X /* x0) . x1 is V11() Element of COMPLEX
((X /* x0) . x1) - (X /. f) is V11() Element of COMPLEX
|.(((X /* x0) . x1) - (X /. f)).| is V11() real ext-real Element of REAL
lim (X /* x0) is V11() Element of COMPLEX
CNS is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of CNS is non empty set
K7( the carrier of CNS,COMPLEX) is complex-valued set
K6(K7( the carrier of CNS,COMPLEX)) is set
X is Relation-like the carrier of CNS -defined COMPLEX -valued Function-like complex-valued Element of K6(K7( the carrier of CNS,COMPLEX))
dom X is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
f is Element of the carrier of CNS
X /. f is V11() Element of COMPLEX
x0 is V11() real ext-real Element of REAL
p is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
p + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative Element of REAL
1 / (p + 1) is V11() real ext-real non negative Element of REAL
(p + 1) " is V11() real ext-real positive non negative Element of REAL
x1 is Element of the carrier of CNS
x1 - f is Element of the carrier of CNS
||.(x1 - f).|| is V11() real ext-real Element of REAL
X /. x1 is V11() Element of COMPLEX
(X /. x1) - (X /. f) is V11() Element of COMPLEX
|.((X /. x1) - (X /. f)).| is V11() real ext-real Element of REAL
K7(NAT, the carrier of CNS) is set
K6(K7(NAT, the carrier of CNS)) is set
p is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
x1 is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
rng x1 is Element of K6( the carrier of CNS)
dom x1 is V45() V46() V47() V48() V49() V50() Element of K6(NAT)
x2 is set
s9 is set
x1 . s9 is set
x2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
x1 . x2 is Element of the carrier of CNS
X /. (x1 . x2) is V11() Element of COMPLEX
(X /. (x1 . x2)) - (X /. f) is V11() Element of COMPLEX
|.((X /. (x1 . x2)) - (X /. f)).| is V11() real ext-real Element of REAL
X /* x1 is non empty Relation-like NAT -defined COMPLEX -valued Function-like total quasi_total complex-valued Element of K6(K7(NAT,COMPLEX))
(X /* x1) . x2 is V11() Element of COMPLEX
((X /* x1) . x2) - (X /. f) is V11() Element of COMPLEX
|.(((X /* x1) . x2) - (X /. f)).| is V11() real ext-real Element of REAL
x2 is V11() real ext-real Element of REAL
x2 " is V11() real ext-real Element of REAL
s9 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
s9 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative Element of REAL
(x2 ") + 0 is V11() real ext-real Element of REAL
1 / (x2 ") is V11() real ext-real Element of REAL
1 / (s9 + 1) is V11() real ext-real non negative Element of REAL
x1 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
x1 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
x1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative Element of REAL
x1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative Element of REAL
1 / (x1 + 1) is V11() real ext-real non negative Element of REAL
1 / (x1 + 1) is V11() real ext-real non negative Element of REAL
x1 . x1 is Element of the carrier of CNS
(x1 . x1) - f is Element of the carrier of CNS
||.((x1 . x1) - f).|| is V11() real ext-real Element of REAL
lim x1 is Element of the carrier of CNS
lim (X /* x1) is V11() Element of COMPLEX
x2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
(X /* x1) . x2 is V11() Element of COMPLEX
((X /* x1) . x2) - (X /. f) is V11() Element of COMPLEX
|.(((X /* x1) . x2) - (X /. f)).| is V11() real ext-real Element of REAL
K7(NAT, the carrier of CNS) is set
K6(K7(NAT, the carrier of CNS)) is set
x0 is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
rng x0 is Element of K6( the carrier of CNS)
lim x0 is Element of the carrier of CNS
p is V11() real ext-real Element of REAL
x1 is V11() real ext-real Element of REAL
x2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
s9 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
x1 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
x0 . x1 is Element of the carrier of CNS
(x0 . x1) - f is Element of the carrier of CNS
||.((x0 . x1) - f).|| is V11() real ext-real Element of REAL
dom x0 is V45() V46() V47() V48() V49() V50() Element of K6(NAT)
X /. (x0 . x1) is V11() Element of COMPLEX
(X /. (x0 . x1)) - (X /. f) is V11() Element of COMPLEX
|.((X /. (x0 . x1)) - (X /. f)).| is V11() real ext-real Element of REAL
X /* x0 is non empty Relation-like NAT -defined COMPLEX -valued Function-like total quasi_total complex-valued Element of K6(K7(NAT,COMPLEX))
(X /* x0) . x1 is V11() Element of COMPLEX
((X /* x0) . x1) - (X /. f) is V11() Element of COMPLEX
|.(((X /* x0) . x1) - (X /. f)).| is V11() real ext-real Element of REAL
lim (X /* x0) is V11() Element of COMPLEX
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of X is non empty set
K7( the carrier of CNS, the carrier of X) is set
K6(K7( the carrier of CNS, the carrier of X)) is set
f is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
dom f is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
x0 is Element of the carrier of CNS
f /. x0 is Element of the carrier of X
p is (X,f /. x0)
x1 is V11() real ext-real Element of REAL
{ b₁ where b₁ is Element of the carrier of X : not x1 <= ||.(b₁ - (f /. x0)).|| } is set
x2 is V11() real ext-real Element of REAL
{ b₁ where b₁ is Element of the carrier of CNS : not x2 <= ||.(b₁ - x0).|| } is set
s9 is (CNS,x0)
x1 is Element of the carrier of CNS
f /. x1 is Element of the carrier of X
(f /. x1) - (f /. x0) is Element of the carrier of X
||.((f /. x1) - (f /. x0)).|| is V11() real ext-real Element of REAL
x1 is Element of the carrier of CNS
x1 - x0 is Element of the carrier of CNS
||.(x1 - x0).|| is V11() real ext-real Element of REAL
p is V11() real ext-real Element of REAL
{ b₁ where b₁ is Element of the carrier of X : not p <= ||.(b₁ - (f /. x0)).|| } is set
x1 is (X,f /. x0)
x2 is (CNS,x0)
s9 is V11() real ext-real Element of REAL
{ b₁ where b₁ is Element of the carrier of CNS : not s9 <= ||.(b₁ - x0).|| } is set
x1 is V11() real ext-real Element of REAL
x1 is Element of the carrier of CNS
x1 - x0 is Element of the carrier of CNS
||.(x1 - x0).|| is V11() real ext-real Element of REAL
f /. x1 is Element of the carrier of X
(f /. x1) - (f /. x0) is Element of the carrier of X
||.((f /. x1) - (f /. x0)).|| is V11() real ext-real Element of REAL
{ b₁ where b₁ is Element of the carrier of CNS : not x1 <= ||.(b₁ - x0).|| } is set
x2 is Element of the carrier of X
x2 - (f /. x0) is Element of the carrier of X
||.(x2 - (f /. x0)).|| is V11() real ext-real Element of REAL
x1 is Element of the carrier of CNS
x1 - x0 is Element of the carrier of CNS
||.(x1 - x0).|| is V11() real ext-real Element of REAL
f /. x1 is Element of the carrier of X
(f /. x1) - (f /. x0) is Element of the carrier of X
||.((f /. x1) - (f /. x0)).|| is V11() real ext-real Element of REAL
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of X is non empty set
K7( the carrier of CNS, the carrier of X) is set
K6(K7( the carrier of CNS, the carrier of X)) is set
f is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
dom f is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
x0 is Element of the carrier of CNS
f /. x0 is Element of the carrier of X
p is Neighbourhood of f /. x0
x1 is V11() real ext-real Element of REAL
{ b₁ where b₁ is Element of the carrier of X : not x1 <= ||.(b₁ - (f /. x0)).|| } is set
x2 is V11() real ext-real Element of REAL
{ b₁ where b₁ is Element of the carrier of CNS : not x2 <= ||.(b₁ - x0).|| } is set
s9 is (CNS,x0)
x1 is Element of the carrier of CNS
f /. x1 is Element of the carrier of X
(f /. x1) - (f /. x0) is Element of the carrier of X
||.((f /. x1) - (f /. x0)).|| is V11() real ext-real Element of REAL
x1 is Element of the carrier of CNS
x1 - x0 is Element of the carrier of CNS
||.(x1 - x0).|| is V11() real ext-real Element of REAL
p is V11() real ext-real Element of REAL
{ b₁ where b₁ is Element of the carrier of X : not p <= ||.(b₁ - (f /. x0)).|| } is set
x1 is Neighbourhood of f /. x0
x2 is (CNS,x0)
s9 is V11() real ext-real Element of REAL
{ b₁ where b₁ is Element of the carrier of CNS : not s9 <= ||.(b₁ - x0).|| } is set
x1 is V11() real ext-real Element of REAL
x1 is Element of the carrier of CNS
x1 - x0 is Element of the carrier of CNS
||.(x1 - x0).|| is V11() real ext-real Element of REAL
f /. x1 is Element of the carrier of X
(f /. x1) - (f /. x0) is Element of the carrier of X
||.((f /. x1) - (f /. x0)).|| is V11() real ext-real Element of REAL
{ b₁ where b₁ is Element of the carrier of CNS : not x1 <= ||.(b₁ - x0).|| } is set
x2 is Element of the carrier of X
x2 - (f /. x0) is Element of the carrier of X
||.(x2 - (f /. x0)).|| is V11() real ext-real Element of REAL
x1 is Element of the carrier of CNS
x1 - x0 is Element of the carrier of CNS
||.(x1 - x0).|| is V11() real ext-real Element of REAL
f /. x1 is Element of the carrier of X
(f /. x1) - (f /. x0) is Element of the carrier of X
||.((f /. x1) - (f /. x0)).|| is V11() real ext-real Element of REAL
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of X is non empty set
K7( the carrier of X, the carrier of CNS) is set
K6(K7( the carrier of X, the carrier of CNS)) is set
f is Relation-like the carrier of X -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of X, the carrier of CNS))
dom f is Element of K6( the carrier of X)
K6( the carrier of X) is set
x0 is Element of the carrier of X
f /. x0 is Element of the carrier of CNS
p is (CNS,f /. x0)
x1 is V11() real ext-real Element of REAL
{ b₁ where b₁ is Element of the carrier of CNS : not x1 <= ||.(b₁ - (f /. x0)).|| } is set
x2 is V11() real ext-real Element of REAL
{ b₁ where b₁ is Element of the carrier of X : not x2 <= ||.(b₁ - x0).|| } is set
s9 is Neighbourhood of x0
x1 is Element of the carrier of X
f /. x1 is Element of the carrier of CNS
(f /. x1) - (f /. x0) is Element of the carrier of CNS
||.((f /. x1) - (f /. x0)).|| is V11() real ext-real Element of REAL
x1 is Element of the carrier of X
x1 - x0 is Element of the carrier of X
||.(x1 - x0).|| is V11() real ext-real Element of REAL
p is V11() real ext-real Element of REAL
{ b₁ where b₁ is Element of the carrier of CNS : not p <= ||.(b₁ - (f /. x0)).|| } is set
x1 is (CNS,f /. x0)
x2 is Neighbourhood of x0
s9 is V11() real ext-real Element of REAL
{ b₁ where b₁ is Element of the carrier of X : not s9 <= ||.(b₁ - x0).|| } is set
x1 is V11() real ext-real Element of REAL
x1 is Element of the carrier of X
x1 - x0 is Element of the carrier of X
||.(x1 - x0).|| is V11() real ext-real Element of REAL
f /. x1 is Element of the carrier of CNS
(f /. x1) - (f /. x0) is Element of the carrier of CNS
||.((f /. x1) - (f /. x0)).|| is V11() real ext-real Element of REAL
{ b₁ where b₁ is Element of the carrier of X : not x1 <= ||.(b₁ - x0).|| } is set
x2 is Element of the carrier of CNS
x2 - (f /. x0) is Element of the carrier of CNS
||.(x2 - (f /. x0)).|| is V11() real ext-real Element of REAL
x1 is Element of the carrier of X
x1 - x0 is Element of the carrier of X
||.(x1 - x0).|| is V11() real ext-real Element of REAL
f /. x1 is Element of the carrier of CNS
(f /. x1) - (f /. x0) is Element of the carrier of CNS
||.((f /. x1) - (f /. x0)).|| is V11() real ext-real Element of REAL
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of X is non empty set
K7( the carrier of CNS, the carrier of X) is set
K6(K7( the carrier of CNS, the carrier of X)) is set
f is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
dom f is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
x0 is Element of the carrier of CNS
f /. x0 is Element of the carrier of X
p is (X,f /. x0)
x1 is (CNS,x0)
f .: x1 is Element of K6( the carrier of X)
K6( the carrier of X) is set
x2 is set
s9 is Element of the carrier of CNS
f . s9 is set
f /. s9 is Element of the carrier of X
p is (X,f /. x0)
x1 is (CNS,x0)
f .: x1 is Element of K6( the carrier of X)
K6( the carrier of X) is set
s9 is Element of the carrier of CNS
x2 is (CNS,x0)
f . s9 is set
f .: x2 is Element of K6( the carrier of X)
f /. s9 is Element of the carrier of X
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of X is non empty set
K7( the carrier of CNS, the carrier of X) is set
K6(K7( the carrier of CNS, the carrier of X)) is set
f is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
dom f is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
x0 is Element of the carrier of CNS
f /. x0 is Element of the carrier of X
p is Neighbourhood of f /. x0
x1 is (CNS,x0)
f .: x1 is Element of K6( the carrier of X)
K6( the carrier of X) is set
x2 is set
s9 is Element of the carrier of CNS
f . s9 is set
f /. s9 is Element of the carrier of X
p is Neighbourhood of f /. x0
x1 is (CNS,x0)
f .: x1 is Element of K6( the carrier of X)
K6( the carrier of X) is set
s9 is Element of the carrier of CNS
x2 is (CNS,x0)
f . s9 is set
f .: x2 is Element of K6( the carrier of X)
f /. s9 is Element of the carrier of X
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of X is non empty set
K7( the carrier of X, the carrier of CNS) is set
K6(K7( the carrier of X, the carrier of CNS)) is set
f is Relation-like the carrier of X -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of X, the carrier of CNS))
dom f is Element of K6( the carrier of X)
K6( the carrier of X) is set
x0 is Element of the carrier of X
f /. x0 is Element of the carrier of CNS
p is (CNS,f /. x0)
x1 is Neighbourhood of x0
f .: x1 is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
x2 is set
s9 is Element of the carrier of X
f . s9 is set
f /. s9 is Element of the carrier of CNS
p is (CNS,f /. x0)
x1 is Neighbourhood of x0
f .: x1 is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
s9 is Element of the carrier of X
x2 is Neighbourhood of x0
f . s9 is set
f .: x2 is Element of K6( the carrier of CNS)
f /. s9 is Element of the carrier of CNS
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of X is non empty set
K7( the carrier of CNS, the carrier of X) is set
K6(K7( the carrier of CNS, the carrier of X)) is set
f is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
dom f is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
x0 is Element of the carrier of CNS
{x0} is non empty set
p is (CNS,x0)
(dom f) /\ p is Element of K6( the carrier of CNS)
f /. x0 is Element of the carrier of X
x1 is (X,f /. x0)
x2 is (CNS,x0)
f .: x2 is Element of K6( the carrier of X)
K6( the carrier of X) is set
Im (f,x0) is set
f .: {x0} is set
f . x0 is set
{(f . x0)} is non empty set
{(f /. x0)} is non empty set
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of X is non empty set
K7( the carrier of CNS, the carrier of X) is set
K6(K7( the carrier of CNS, the carrier of X)) is set
f is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
dom f is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
x0 is Element of the carrier of CNS
{x0} is non empty set
p is (CNS,x0)
(dom f) /\ p is Element of K6( the carrier of CNS)
f /. x0 is Element of the carrier of X
x1 is Neighbourhood of f /. x0
x2 is (CNS,x0)
f .: x2 is Element of K6( the carrier of X)
K6( the carrier of X) is set
Im (f,x0) is set
f .: {x0} is set
f . x0 is set
{(f . x0)} is non empty set
{(f /. x0)} is non empty set
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of X is non empty set
K7( the carrier of X, the carrier of CNS) is set
K6(K7( the carrier of X, the carrier of CNS)) is set
f is Relation-like the carrier of X -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of X, the carrier of CNS))
dom f is Element of K6( the carrier of X)
K6( the carrier of X) is set
x0 is Element of the carrier of X
{x0} is non empty set
p is Neighbourhood of x0
(dom f) /\ p is Element of K6( the carrier of X)
f /. x0 is Element of the carrier of CNS
x1 is (CNS,f /. x0)
x2 is Neighbourhood of x0
f .: x2 is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
Im (f,x0) is set
f .: {x0} is set
f . x0 is set
{(f . x0)} is non empty set
{(f /. x0)} is non empty set
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
K7(NAT, the carrier of CNS) is set
K6(K7(NAT, the carrier of CNS)) is set
X is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of X is non empty set
K7( the carrier of CNS, the carrier of X) is set
K6(K7( the carrier of CNS, the carrier of X)) is set
f is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
dom f is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
x0 is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
dom x0 is Element of K6( the carrier of CNS)
(dom f) /\ (dom x0) is Element of K6( the carrier of CNS)
f + x0 is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
f - x0 is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
p is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
rng p is Element of K6( the carrier of CNS)
(f + x0) /* p is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
K7(NAT, the carrier of X) is set
K6(K7(NAT, the carrier of X)) is set
f /* p is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
x0 /* p is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
(f /* p) + (x0 /* p) is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
(f - x0) /* p is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
(f /* p) - (x0 /* p) is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
dom (f + x0) is Element of K6( the carrier of CNS)
x1 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
p . x1 is Element of the carrier of CNS
((f + x0) /* p) . x1 is Element of the carrier of X
(f + x0) /. (p . x1) is Element of the carrier of X
f /. (p . x1) is Element of the carrier of X
x0 /. (p . x1) is Element of the carrier of X
(f /. (p . x1)) + (x0 /. (p . x1)) is Element of the carrier of X
(f /* p) . x1 is Element of the carrier of X
((f /* p) . x1) + (x0 /. (p . x1)) is Element of the carrier of X
(x0 /* p) . x1 is Element of the carrier of X
((f /* p) . x1) + ((x0 /* p) . x1) is Element of the carrier of X
dom (f - x0) is Element of K6( the carrier of CNS)
x1 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
p . x1 is Element of the carrier of CNS
((f - x0) /* p) . x1 is Element of the carrier of X
(f - x0) /. (p . x1) is Element of the carrier of X
f /. (p . x1) is Element of the carrier of X
x0 /. (p . x1) is Element of the carrier of X
(f /. (p . x1)) - (x0 /. (p . x1)) is Element of the carrier of X
(f /* p) . x1 is Element of the carrier of X
((f /* p) . x1) - (x0 /. (p . x1)) is Element of the carrier of X
(x0 /* p) . x1 is Element of the carrier of X
((f /* p) . x1) - ((x0 /* p) . x1) is Element of the carrier of X
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
K7(NAT, the carrier of CNS) is set
K6(K7(NAT, the carrier of CNS)) is set
X is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of X is non empty set
K7( the carrier of CNS, the carrier of X) is set
K6(K7( the carrier of CNS, the carrier of X)) is set
f is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
dom f is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
x0 is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
dom x0 is Element of K6( the carrier of CNS)
(dom f) /\ (dom x0) is Element of K6( the carrier of CNS)
f + x0 is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
f - x0 is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
p is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
rng p is Element of K6( the carrier of CNS)
(f + x0) /* p is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
K7(NAT, the carrier of X) is set
K6(K7(NAT, the carrier of X)) is set
f /* p is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
x0 /* p is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
(f /* p) + (x0 /* p) is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
(f - x0) /* p is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
(f /* p) - (x0 /* p) is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
dom (f + x0) is Element of K6( the carrier of CNS)
x1 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
p . x1 is Element of the carrier of CNS
((f + x0) /* p) . x1 is Element of the carrier of X
(f + x0) /. (p . x1) is Element of the carrier of X
f /. (p . x1) is Element of the carrier of X
x0 /. (p . x1) is Element of the carrier of X
(f /. (p . x1)) + (x0 /. (p . x1)) is Element of the carrier of X
(f /* p) . x1 is Element of the carrier of X
((f /* p) . x1) + (x0 /. (p . x1)) is Element of the carrier of X
(x0 /* p) . x1 is Element of the carrier of X
((f /* p) . x1) + ((x0 /* p) . x1) is Element of the carrier of X
dom (f - x0) is Element of K6( the carrier of CNS)
x1 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
p . x1 is Element of the carrier of CNS
((f - x0) /* p) . x1 is Element of the carrier of X
(f - x0) /. (p . x1) is Element of the carrier of X
f /. (p . x1) is Element of the carrier of X
x0 /. (p . x1) is Element of the carrier of X
(f /. (p . x1)) - (x0 /. (p . x1)) is Element of the carrier of X
(f /* p) . x1 is Element of the carrier of X
((f /* p) . x1) - (x0 /. (p . x1)) is Element of the carrier of X
(x0 /* p) . x1 is Element of the carrier of X
((f /* p) . x1) - ((x0 /* p) . x1) is Element of the carrier of X
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of X is non empty set
K7( the carrier of X, the carrier of CNS) is set
K6(K7( the carrier of X, the carrier of CNS)) is set
K7(NAT, the carrier of X) is set
K6(K7(NAT, the carrier of X)) is set
f is Relation-like the carrier of X -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of X, the carrier of CNS))
dom f is Element of K6( the carrier of X)
K6( the carrier of X) is set
x0 is Relation-like the carrier of X -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of X, the carrier of CNS))
dom x0 is Element of K6( the carrier of X)
(dom f) /\ (dom x0) is Element of K6( the carrier of X)
f + x0 is Relation-like the carrier of X -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of X, the carrier of CNS))
f - x0 is Relation-like the carrier of X -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of X, the carrier of CNS))
p is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
rng p is Element of K6( the carrier of X)
(f + x0) /* p is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
K7(NAT, the carrier of CNS) is set
K6(K7(NAT, the carrier of CNS)) is set
f /* p is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
x0 /* p is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
(f /* p) + (x0 /* p) is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
(f - x0) /* p is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
(f /* p) - (x0 /* p) is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
dom (f + x0) is Element of K6( the carrier of X)
x1 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
p . x1 is Element of the carrier of X
((f + x0) /* p) . x1 is Element of the carrier of CNS
(f + x0) /. (p . x1) is Element of the carrier of CNS
f /. (p . x1) is Element of the carrier of CNS
x0 /. (p . x1) is Element of the carrier of CNS
(f /. (p . x1)) + (x0 /. (p . x1)) is Element of the carrier of CNS
(f /* p) . x1 is Element of the carrier of CNS
((f /* p) . x1) + (x0 /. (p . x1)) is Element of the carrier of CNS
(x0 /* p) . x1 is Element of the carrier of CNS
((f /* p) . x1) + ((x0 /* p) . x1) is Element of the carrier of CNS
dom (f - x0) is Element of K6( the carrier of X)
x1 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
p . x1 is Element of the carrier of X
((f - x0) /* p) . x1 is Element of the carrier of CNS
(f - x0) /. (p . x1) is Element of the carrier of CNS
f /. (p . x1) is Element of the carrier of CNS
x0 /. (p . x1) is Element of the carrier of CNS
(f /. (p . x1)) - (x0 /. (p . x1)) is Element of the carrier of CNS
(f /* p) . x1 is Element of the carrier of CNS
((f /* p) . x1) - (x0 /. (p . x1)) is Element of the carrier of CNS
(x0 /* p) . x1 is Element of the carrier of CNS
((f /* p) . x1) - ((x0 /* p) . x1) is Element of the carrier of CNS
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
K7(NAT, the carrier of CNS) is set
K6(K7(NAT, the carrier of CNS)) is set
X is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of X is non empty set
K7( the carrier of CNS, the carrier of X) is set
K6(K7( the carrier of CNS, the carrier of X)) is set
f is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
dom f is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
x0 is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
rng x0 is Element of K6( the carrier of CNS)
f /* x0 is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
K7(NAT, the carrier of X) is set
K6(K7(NAT, the carrier of X)) is set
p is V11() set
p (#) f is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
(p (#) f) /* x0 is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
p * (f /* x0) is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
dom (p (#) f) is Element of K6( the carrier of CNS)
x1 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
x0 . x1 is Element of the carrier of CNS
((p (#) f) /* x0) . x1 is Element of the carrier of X
(p (#) f) /. (x0 . x1) is Element of the carrier of X
f /. (x0 . x1) is Element of the carrier of X
p * (f /. (x0 . x1)) is Element of the carrier of X
(f /* x0) . x1 is Element of the carrier of X
p * ((f /* x0) . x1) is Element of the carrier of X
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
K7(NAT, the carrier of CNS) is set
K6(K7(NAT, the carrier of CNS)) is set
X is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of X is non empty set
K7( the carrier of CNS, the carrier of X) is set
K6(K7( the carrier of CNS, the carrier of X)) is set
f is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
dom f is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
x0 is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
rng x0 is Element of K6( the carrier of CNS)
f /* x0 is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
K7(NAT, the carrier of X) is set
K6(K7(NAT, the carrier of X)) is set
p is V11() real ext-real Element of REAL
p (#) f is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
(p (#) f) /* x0 is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
p * (f /* x0) is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
dom (p (#) f) is Element of K6( the carrier of CNS)
x1 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
x0 . x1 is Element of the carrier of CNS
((p (#) f) /* x0) . x1 is Element of the carrier of X
(p (#) f) /. (x0 . x1) is Element of the carrier of X
f /. (x0 . x1) is Element of the carrier of X
p * (f /. (x0 . x1)) is Element of the carrier of X
(f /* x0) . x1 is Element of the carrier of X
p * ((f /* x0) . x1) is Element of the carrier of X
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of X is non empty set
K7( the carrier of X, the carrier of CNS) is set
K6(K7( the carrier of X, the carrier of CNS)) is set
K7(NAT, the carrier of X) is set
K6(K7(NAT, the carrier of X)) is set
f is Relation-like the carrier of X -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of X, the carrier of CNS))
dom f is Element of K6( the carrier of X)
K6( the carrier of X) is set
x0 is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
rng x0 is Element of K6( the carrier of X)
f /* x0 is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
K7(NAT, the carrier of CNS) is set
K6(K7(NAT, the carrier of CNS)) is set
p is V11() set
p (#) f is Relation-like the carrier of X -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of X, the carrier of CNS))
(p (#) f) /* x0 is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
p * (f /* x0) is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
dom (p (#) f) is Element of K6( the carrier of X)
x1 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
x0 . x1 is Element of the carrier of X
((p (#) f) /* x0) . x1 is Element of the carrier of CNS
(p (#) f) /. (x0 . x1) is Element of the carrier of CNS
f /. (x0 . x1) is Element of the carrier of CNS
p * (f /. (x0 . x1)) is Element of the carrier of CNS
(f /* x0) . x1 is Element of the carrier of CNS
p * ((f /* x0) . x1) is Element of the carrier of CNS
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
K7(NAT, the carrier of CNS) is set
K6(K7(NAT, the carrier of CNS)) is set
X is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of X is non empty set
K7( the carrier of CNS, the carrier of X) is set
K6(K7( the carrier of CNS, the carrier of X)) is set
f is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
dom f is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
||.f.|| is Relation-like the carrier of CNS -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7( the carrier of CNS,REAL))
K7( the carrier of CNS,REAL) is complex-valued ext-real-valued real-valued set
K6(K7( the carrier of CNS,REAL)) is set
- f is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
x0 is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
rng x0 is Element of K6( the carrier of CNS)
f /* x0 is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
K7(NAT, the carrier of X) is set
K6(K7(NAT, the carrier of X)) is set
||.(f /* x0).|| is non empty Relation-like NAT -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
||.f.|| /* x0 is non empty Relation-like NAT -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
- (f /* x0) is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
(- f) /* x0 is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
dom ||.f.|| is Element of K6( the carrier of CNS)
p is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
x0 . p is Element of the carrier of CNS
||.(f /* x0).|| . p is V11() real ext-real Element of REAL
(f /* x0) . p is Element of the carrier of X
||.((f /* x0) . p).|| is V11() real ext-real Element of REAL
f /. (x0 . p) is Element of the carrier of X
||.(f /. (x0 . p)).|| is V11() real ext-real Element of REAL
||.f.|| . (x0 . p) is V11() real ext-real Element of REAL
||.f.|| /. (x0 . p) is V11() real ext-real Element of REAL
(||.f.|| /* x0) . p is V11() real ext-real Element of REAL
(- 1r) * (f /* x0) is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
(- 1r) (#) f is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
((- 1r) (#) f) /* x0 is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
K7(NAT, the carrier of CNS) is set
K6(K7(NAT, the carrier of CNS)) is set
X is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of X is non empty set
K7( the carrier of CNS, the carrier of X) is set
K6(K7( the carrier of CNS, the carrier of X)) is set
f is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
dom f is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
||.f.|| is Relation-like the carrier of CNS -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7( the carrier of CNS,REAL))
K7( the carrier of CNS,REAL) is complex-valued ext-real-valued real-valued set
K6(K7( the carrier of CNS,REAL)) is set
- f is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
x0 is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
rng x0 is Element of K6( the carrier of CNS)
f /* x0 is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
K7(NAT, the carrier of X) is set
K6(K7(NAT, the carrier of X)) is set
||.(f /* x0).|| is non empty Relation-like NAT -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
||.f.|| /* x0 is non empty Relation-like NAT -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
- (f /* x0) is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
(- f) /* x0 is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
dom ||.f.|| is Element of K6( the carrier of CNS)
p is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
x0 . p is Element of the carrier of CNS
||.(f /* x0).|| . p is V11() real ext-real Element of REAL
(f /* x0) . p is Element of the carrier of X
||.((f /* x0) . p).|| is V11() real ext-real Element of REAL
f /. (x0 . p) is Element of the carrier of X
||.(f /. (x0 . p)).|| is V11() real ext-real Element of REAL
||.f.|| . (x0 . p) is V11() real ext-real Element of REAL
||.f.|| /. (x0 . p) is V11() real ext-real Element of REAL
(||.f.|| /* x0) . p is V11() real ext-real Element of REAL
(- 1) * (f /* x0) is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
(- 1) (#) f is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
((- 1) (#) f) /* x0 is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of X is non empty set
K7( the carrier of X, the carrier of CNS) is set
K6(K7( the carrier of X, the carrier of CNS)) is set
K7(NAT, the carrier of X) is set
K6(K7(NAT, the carrier of X)) is set
f is Relation-like the carrier of X -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of X, the carrier of CNS))
dom f is Element of K6( the carrier of X)
K6( the carrier of X) is set
||.f.|| is Relation-like the carrier of X -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7( the carrier of X,REAL))
K7( the carrier of X,REAL) is complex-valued ext-real-valued real-valued set
K6(K7( the carrier of X,REAL)) is set
- f is Relation-like the carrier of X -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of X, the carrier of CNS))
x0 is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
rng x0 is Element of K6( the carrier of X)
f /* x0 is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
K7(NAT, the carrier of CNS) is set
K6(K7(NAT, the carrier of CNS)) is set
||.(f /* x0).|| is non empty Relation-like NAT -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
||.f.|| /* x0 is non empty Relation-like NAT -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
- (f /* x0) is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
(- f) /* x0 is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
dom ||.f.|| is Element of K6( the carrier of X)
p is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
x0 . p is Element of the carrier of X
||.(f /* x0).|| . p is V11() real ext-real Element of REAL
(f /* x0) . p is Element of the carrier of CNS
||.((f /* x0) . p).|| is V11() real ext-real Element of REAL
f /. (x0 . p) is Element of the carrier of CNS
||.(f /. (x0 . p)).|| is V11() real ext-real Element of REAL
||.f.|| . (x0 . p) is V11() real ext-real Element of REAL
||.f.|| /. (x0 . p) is V11() real ext-real Element of REAL
(||.f.|| /* x0) . p is V11() real ext-real Element of REAL
(- 1r) * (f /* x0) is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
(- 1r) (#) f is Relation-like the carrier of X -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of X, the carrier of CNS))
((- 1r) (#) f) /* x0 is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of X is non empty set
K7( the carrier of CNS, the carrier of X) is set
K6(K7( the carrier of CNS, the carrier of X)) is set
f is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
x0 is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
f + x0 is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
f - x0 is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
p is Element of the carrier of CNS
dom f is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
dom x0 is Element of K6( the carrier of CNS)
(dom f) /\ (dom x0) is Element of K6( the carrier of CNS)
dom (f + x0) is Element of K6( the carrier of CNS)
K7(NAT, the carrier of CNS) is set
K6(K7(NAT, the carrier of CNS)) is set
x1 is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
rng x1 is Element of K6( the carrier of CNS)
lim x1 is Element of the carrier of CNS
x0 /* x1 is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
K7(NAT, the carrier of X) is set
K6(K7(NAT, the carrier of X)) is set
f /* x1 is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
(f /* x1) + (x0 /* x1) is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
(f + x0) /* x1 is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
f /. p is Element of the carrier of X
lim (f /* x1) is Element of the carrier of X
x0 /. p is Element of the carrier of X
lim (x0 /* x1) is Element of the carrier of X
(f + x0) /. p is Element of the carrier of X
(f /. p) + (x0 /. p) is Element of the carrier of X
lim ((f /* x1) + (x0 /* x1)) is Element of the carrier of X
lim ((f + x0) /* x1) is Element of the carrier of X
dom (f - x0) is Element of K6( the carrier of CNS)
x1 is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
rng x1 is Element of K6( the carrier of CNS)
lim x1 is Element of the carrier of CNS
x0 /* x1 is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
f /* x1 is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
(f /* x1) - (x0 /* x1) is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
(f - x0) /* x1 is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
lim (f /* x1) is Element of the carrier of X
lim (x0 /* x1) is Element of the carrier of X
(f - x0) /. p is Element of the carrier of X
(f /. p) - (x0 /. p) is Element of the carrier of X
lim ((f /* x1) - (x0 /* x1)) is Element of the carrier of X
lim ((f - x0) /* x1) is Element of the carrier of X
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of X is non empty set
K7( the carrier of CNS, the carrier of X) is set
K6(K7( the carrier of CNS, the carrier of X)) is set
f is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
x0 is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
f + x0 is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
f - x0 is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
p is Element of the carrier of CNS
dom f is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
dom x0 is Element of K6( the carrier of CNS)
(dom f) /\ (dom x0) is Element of K6( the carrier of CNS)
dom (f + x0) is Element of K6( the carrier of CNS)
K7(NAT, the carrier of CNS) is set
K6(K7(NAT, the carrier of CNS)) is set
x1 is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
rng x1 is Element of K6( the carrier of CNS)
lim x1 is Element of the carrier of CNS
x0 /* x1 is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
K7(NAT, the carrier of X) is set
K6(K7(NAT, the carrier of X)) is set
f /* x1 is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
(f /* x1) + (x0 /* x1) is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
(f + x0) /* x1 is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
f /. p is Element of the carrier of X
lim (f /* x1) is Element of the carrier of X
x0 /. p is Element of the carrier of X
lim (x0 /* x1) is Element of the carrier of X
(f + x0) /. p is Element of the carrier of X
(f /. p) + (x0 /. p) is Element of the carrier of X
lim ((f /* x1) + (x0 /* x1)) is Element of the carrier of X
lim ((f + x0) /* x1) is Element of the carrier of X
dom (f - x0) is Element of K6( the carrier of CNS)
x1 is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
rng x1 is Element of K6( the carrier of CNS)
lim x1 is Element of the carrier of CNS
x0 /* x1 is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
f /* x1 is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
(f /* x1) - (x0 /* x1) is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
(f - x0) /* x1 is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
lim (f /* x1) is Element of the carrier of X
lim (x0 /* x1) is Element of the carrier of X
(f - x0) /. p is Element of the carrier of X
(f /. p) - (x0 /. p) is Element of the carrier of X
lim ((f /* x1) - (x0 /* x1)) is Element of the carrier of X
lim ((f - x0) /* x1) is Element of the carrier of X
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of X is non empty set
K7( the carrier of X, the carrier of CNS) is set
K6(K7( the carrier of X, the carrier of CNS)) is set
f is Relation-like the carrier of X -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of X, the carrier of CNS))
x0 is Relation-like the carrier of X -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of X, the carrier of CNS))
f + x0 is Relation-like the carrier of X -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of X, the carrier of CNS))
f - x0 is Relation-like the carrier of X -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of X, the carrier of CNS))
p is Element of the carrier of X
dom f is Element of K6( the carrier of X)
K6( the carrier of X) is set
dom x0 is Element of K6( the carrier of X)
(dom f) /\ (dom x0) is Element of K6( the carrier of X)
dom (f + x0) is Element of K6( the carrier of X)
K7(NAT, the carrier of X) is set
K6(K7(NAT, the carrier of X)) is set
x1 is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
rng x1 is Element of K6( the carrier of X)
lim x1 is Element of the carrier of X
x0 /* x1 is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
K7(NAT, the carrier of CNS) is set
K6(K7(NAT, the carrier of CNS)) is set
f /* x1 is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
(f /* x1) + (x0 /* x1) is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
(f + x0) /* x1 is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
f /. p is Element of the carrier of CNS
lim (f /* x1) is Element of the carrier of CNS
x0 /. p is Element of the carrier of CNS
lim (x0 /* x1) is Element of the carrier of CNS
(f + x0) /. p is Element of the carrier of CNS
(f /. p) + (x0 /. p) is Element of the carrier of CNS
lim ((f /* x1) + (x0 /* x1)) is Element of the carrier of CNS
lim ((f + x0) /* x1) is Element of the carrier of CNS
dom (f - x0) is Element of K6( the carrier of X)
x1 is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
rng x1 is Element of K6( the carrier of X)
lim x1 is Element of the carrier of X
x0 /* x1 is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
f /* x1 is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
(f /* x1) - (x0 /* x1) is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
(f - x0) /* x1 is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
lim (f /* x1) is Element of the carrier of CNS
lim (x0 /* x1) is Element of the carrier of CNS
(f - x0) /. p is Element of the carrier of CNS
(f /. p) - (x0 /. p) is Element of the carrier of CNS
lim ((f /* x1) - (x0 /* x1)) is Element of the carrier of CNS
lim ((f - x0) /* x1) is Element of the carrier of CNS
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of X is non empty set
K7( the carrier of CNS, the carrier of X) is set
K6(K7( the carrier of CNS, the carrier of X)) is set
f is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
x0 is Element of the carrier of CNS
p is V11() set
p (#) f is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
dom f is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
dom (p (#) f) is Element of K6( the carrier of CNS)
K7(NAT, the carrier of CNS) is set
K6(K7(NAT, the carrier of CNS)) is set
(p (#) f) /. x0 is Element of the carrier of X
x1 is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
rng x1 is Element of K6( the carrier of CNS)
lim x1 is Element of the carrier of CNS
(p (#) f) /* x1 is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
K7(NAT, the carrier of X) is set
K6(K7(NAT, the carrier of X)) is set
lim ((p (#) f) /* x1) is Element of the carrier of X
f /. x0 is Element of the carrier of X
f /* x1 is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
lim (f /* x1) is Element of the carrier of X
p * (f /* x1) is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
p * (f /. x0) is Element of the carrier of X
lim (p * (f /* x1)) is Element of the carrier of X
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of X is non empty set
K7( the carrier of CNS, the carrier of X) is set
K6(K7( the carrier of CNS, the carrier of X)) is set
f is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
x0 is Element of the carrier of CNS
p is V11() real ext-real Element of REAL
p (#) f is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
dom f is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
dom (p (#) f) is Element of K6( the carrier of CNS)
K7(NAT, the carrier of CNS) is set
K6(K7(NAT, the carrier of CNS)) is set
(p (#) f) /. x0 is Element of the carrier of X
x1 is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
rng x1 is Element of K6( the carrier of CNS)
lim x1 is Element of the carrier of CNS
(p (#) f) /* x1 is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
K7(NAT, the carrier of X) is set
K6(K7(NAT, the carrier of X)) is set
lim ((p (#) f) /* x1) is Element of the carrier of X
f /. x0 is Element of the carrier of X
f /* x1 is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
lim (f /* x1) is Element of the carrier of X
p * (f /* x1) is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
p * (f /. x0) is Element of the carrier of X
lim (p * (f /* x1)) is Element of the carrier of X
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of X is non empty set
K7( the carrier of X, the carrier of CNS) is set
K6(K7( the carrier of X, the carrier of CNS)) is set
f is Relation-like the carrier of X -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of X, the carrier of CNS))
x0 is Element of the carrier of X
p is V11() set
p (#) f is Relation-like the carrier of X -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of X, the carrier of CNS))
dom f is Element of K6( the carrier of X)
K6( the carrier of X) is set
dom (p (#) f) is Element of K6( the carrier of X)
K7(NAT, the carrier of X) is set
K6(K7(NAT, the carrier of X)) is set
(p (#) f) /. x0 is Element of the carrier of CNS
x1 is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
rng x1 is Element of K6( the carrier of X)
lim x1 is Element of the carrier of X
(p (#) f) /* x1 is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
K7(NAT, the carrier of CNS) is set
K6(K7(NAT, the carrier of CNS)) is set
lim ((p (#) f) /* x1) is Element of the carrier of CNS
f /. x0 is Element of the carrier of CNS
f /* x1 is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
lim (f /* x1) is Element of the carrier of CNS
p * (f /* x1) is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
p * (f /. x0) is Element of the carrier of CNS
lim (p * (f /* x1)) is Element of the carrier of CNS
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of X is non empty set
K7( the carrier of CNS, the carrier of X) is set
K6(K7( the carrier of CNS, the carrier of X)) is set
f is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
||.f.|| is Relation-like the carrier of CNS -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7( the carrier of CNS,REAL))
K7( the carrier of CNS,REAL) is complex-valued ext-real-valued real-valued set
K6(K7( the carrier of CNS,REAL)) is set
- f is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
x0 is Element of the carrier of CNS
dom f is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
dom ||.f.|| is Element of K6( the carrier of CNS)
K7(NAT, the carrier of CNS) is set
K6(K7(NAT, the carrier of CNS)) is set
p is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
rng p is Element of K6( the carrier of CNS)
lim p is Element of the carrier of CNS
f /. x0 is Element of the carrier of X
f /* p is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
K7(NAT, the carrier of X) is set
K6(K7(NAT, the carrier of X)) is set
lim (f /* p) is Element of the carrier of X
||.(f /* p).|| is non empty Relation-like NAT -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
||.f.|| /* p is non empty Relation-like NAT -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
||.f.|| /. x0 is V11() real ext-real Element of REAL
||.f.|| . x0 is V11() real ext-real Element of REAL
||.(f /. x0).|| is V11() real ext-real Element of REAL
lim ||.(f /* p).|| is V11() real ext-real Element of REAL
lim (||.f.|| /* p) is V11() real ext-real Element of REAL
(- 1r) (#) f is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of X is non empty set
K7( the carrier of CNS, the carrier of X) is set
K6(K7( the carrier of CNS, the carrier of X)) is set
f is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
||.f.|| is Relation-like the carrier of CNS -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7( the carrier of CNS,REAL))
K7( the carrier of CNS,REAL) is complex-valued ext-real-valued real-valued set
K6(K7( the carrier of CNS,REAL)) is set
- f is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
x0 is Element of the carrier of CNS
dom f is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
dom ||.f.|| is Element of K6( the carrier of CNS)
K7(NAT, the carrier of CNS) is set
K6(K7(NAT, the carrier of CNS)) is set
p is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
rng p is Element of K6( the carrier of CNS)
lim p is Element of the carrier of CNS
f /. x0 is Element of the carrier of X
f /* p is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
K7(NAT, the carrier of X) is set
K6(K7(NAT, the carrier of X)) is set
lim (f /* p) is Element of the carrier of X
||.(f /* p).|| is non empty Relation-like NAT -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
||.f.|| /* p is non empty Relation-like NAT -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
||.f.|| /. x0 is V11() real ext-real Element of REAL
||.f.|| . x0 is V11() real ext-real Element of REAL
||.(f /. x0).|| is V11() real ext-real Element of REAL
lim ||.(f /* p).|| is V11() real ext-real Element of REAL
lim (||.f.|| /* p) is V11() real ext-real Element of REAL
(- 1) (#) f is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of X is non empty set
K7( the carrier of X, the carrier of CNS) is set
K6(K7( the carrier of X, the carrier of CNS)) is set
f is Relation-like the carrier of X -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of X, the carrier of CNS))
||.f.|| is Relation-like the carrier of X -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7( the carrier of X,REAL))
K7( the carrier of X,REAL) is complex-valued ext-real-valued real-valued set
K6(K7( the carrier of X,REAL)) is set
- f is Relation-like the carrier of X -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of X, the carrier of CNS))
x0 is Element of the carrier of X
dom f is Element of K6( the carrier of X)
K6( the carrier of X) is set
dom ||.f.|| is Element of K6( the carrier of X)
K7(NAT, the carrier of X) is set
K6(K7(NAT, the carrier of X)) is set
p is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
rng p is Element of K6( the carrier of X)
lim p is Element of the carrier of X
f /. x0 is Element of the carrier of CNS
f /* p is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
K7(NAT, the carrier of CNS) is set
K6(K7(NAT, the carrier of CNS)) is set
lim (f /* p) is Element of the carrier of CNS
||.(f /* p).|| is non empty Relation-like NAT -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
||.f.|| /* p is non empty Relation-like NAT -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
||.f.|| /. x0 is V11() real ext-real Element of REAL
||.f.|| . x0 is V11() real ext-real Element of REAL
||.(f /. x0).|| is V11() real ext-real Element of REAL
lim ||.(f /* p).|| is V11() real ext-real Element of REAL
lim (||.f.|| /* p) is V11() real ext-real Element of REAL
(- 1r) (#) f is Relation-like the carrier of X -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of X, the carrier of CNS))
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of X is non empty set
K7( the carrier of CNS, the carrier of X) is set
K6(K7( the carrier of CNS, the carrier of X)) is set
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of X is non empty set
K7( the carrier of CNS, the carrier of X) is set
K6(K7( the carrier of CNS, the carrier of X)) is set
CNS is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of X is non empty set
K7( the carrier of CNS, the carrier of X) is set
K6(K7( the carrier of CNS, the carrier of X)) is set
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
K7( the carrier of CNS,COMPLEX) is complex-valued set
K6(K7( the carrier of CNS,COMPLEX)) is set
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
K7( the carrier of CNS,REAL) is complex-valued ext-real-valued real-valued set
K6(K7( the carrier of CNS,REAL)) is set
CNS is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of CNS is non empty set
K7( the carrier of CNS,COMPLEX) is complex-valued set
K6(K7( the carrier of CNS,COMPLEX)) is set
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
K7(NAT, the carrier of CNS) is set
K6(K7(NAT, the carrier of CNS)) is set
X is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of X is non empty set
K7( the carrier of CNS, the carrier of X) is set
K6(K7( the carrier of CNS, the carrier of X)) is set
f is set
x0 is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
dom x0 is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
p is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
rng p is Element of K6( the carrier of CNS)
lim p is Element of the carrier of CNS
x0 | f is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
dom (x0 | f) is Element of K6( the carrier of CNS)
(dom x0) /\ f is Element of K6( the carrier of CNS)
dom p is V45() V46() V47() V48() V49() V50() Element of K6(NAT)
x1 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
p . x1 is Element of the carrier of CNS
(x0 | f) /* p is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
K7(NAT, the carrier of X) is set
K6(K7(NAT, the carrier of X)) is set
((x0 | f) /* p) . x1 is Element of the carrier of X
(x0 | f) /. (p . x1) is Element of the carrier of X
x0 /. (p . x1) is Element of the carrier of X
x0 /* p is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
(x0 /* p) . x1 is Element of the carrier of X
x0 /. (lim p) is Element of the carrier of X
(x0 | f) /. (lim p) is Element of the carrier of X
lim (x0 /* p) is Element of the carrier of X
p is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
rng p is Element of K6( the carrier of CNS)
lim p is Element of the carrier of CNS
x0 /* p is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
x0 /. (lim p) is Element of the carrier of X
lim (x0 /* p) is Element of the carrier of X
x0 | f is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
dom (x0 | f) is Element of K6( the carrier of CNS)
(dom x0) /\ f is Element of K6( the carrier of CNS)
p is Element of the carrier of CNS
x1 is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
rng x1 is Element of K6( the carrier of CNS)
lim x1 is Element of the carrier of CNS
dom x1 is V45() V46() V47() V48() V49() V50() Element of K6(NAT)
x2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
x1 . x2 is Element of the carrier of CNS
(x0 | f) /* x1 is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
K7(NAT, the carrier of X) is set
K6(K7(NAT, the carrier of X)) is set
((x0 | f) /* x1) . x2 is Element of the carrier of X
(x0 | f) /. (x1 . x2) is Element of the carrier of X
x0 /. (x1 . x2) is Element of the carrier of X
x0 /* x1 is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
(x0 /* x1) . x2 is Element of the carrier of X
(x0 | f) /. (lim x1) is Element of the carrier of X
x0 /. (lim x1) is Element of the carrier of X
lim ((x0 | f) /* x1) is Element of the carrier of X
(x0 | f) /. p is Element of the carrier of X
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
K7(NAT, the carrier of CNS) is set
K6(K7(NAT, the carrier of CNS)) is set
X is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of X is non empty set
K7( the carrier of CNS, the carrier of X) is set
K6(K7( the carrier of CNS, the carrier of X)) is set
f is set
x0 is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
dom x0 is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
p is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
rng p is Element of K6( the carrier of CNS)
lim p is Element of the carrier of CNS
x0 | f is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
dom (x0 | f) is Element of K6( the carrier of CNS)
(dom x0) /\ f is Element of K6( the carrier of CNS)
dom p is V45() V46() V47() V48() V49() V50() Element of K6(NAT)
x1 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
p . x1 is Element of the carrier of CNS
(x0 | f) /* p is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
K7(NAT, the carrier of X) is set
K6(K7(NAT, the carrier of X)) is set
((x0 | f) /* p) . x1 is Element of the carrier of X
(x0 | f) /. (p . x1) is Element of the carrier of X
x0 /. (p . x1) is Element of the carrier of X
x0 /* p is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
(x0 /* p) . x1 is Element of the carrier of X
x0 /. (lim p) is Element of the carrier of X
(x0 | f) /. (lim p) is Element of the carrier of X
lim (x0 /* p) is Element of the carrier of X
p is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
rng p is Element of K6( the carrier of CNS)
lim p is Element of the carrier of CNS
x0 /* p is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
x0 /. (lim p) is Element of the carrier of X
lim (x0 /* p) is Element of the carrier of X
x0 | f is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
dom (x0 | f) is Element of K6( the carrier of CNS)
(dom x0) /\ f is Element of K6( the carrier of CNS)
p is Element of the carrier of CNS
x1 is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
rng x1 is Element of K6( the carrier of CNS)
lim x1 is Element of the carrier of CNS
dom x1 is V45() V46() V47() V48() V49() V50() Element of K6(NAT)
x2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
x1 . x2 is Element of the carrier of CNS
(x0 | f) /* x1 is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
K7(NAT, the carrier of X) is set
K6(K7(NAT, the carrier of X)) is set
((x0 | f) /* x1) . x2 is Element of the carrier of X
(x0 | f) /. (x1 . x2) is Element of the carrier of X
x0 /. (x1 . x2) is Element of the carrier of X
x0 /* x1 is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
(x0 /* x1) . x2 is Element of the carrier of X
(x0 | f) /. (lim x1) is Element of the carrier of X
x0 /. (lim x1) is Element of the carrier of X
lim ((x0 | f) /* x1) is Element of the carrier of X
(x0 | f) /. p is Element of the carrier of X
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of X is non empty set
K7( the carrier of X, the carrier of CNS) is set
K6(K7( the carrier of X, the carrier of CNS)) is set
K7(NAT, the carrier of X) is set
K6(K7(NAT, the carrier of X)) is set
f is set
x0 is Relation-like the carrier of X -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of X, the carrier of CNS))
dom x0 is Element of K6( the carrier of X)
K6( the carrier of X) is set
p is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
rng p is Element of K6( the carrier of X)
lim p is Element of the carrier of X
x0 | f is Relation-like the carrier of X -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of X, the carrier of CNS))
dom (x0 | f) is Element of K6( the carrier of X)
(dom x0) /\ f is Element of K6( the carrier of X)
dom p is V45() V46() V47() V48() V49() V50() Element of K6(NAT)
x1 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
p . x1 is Element of the carrier of X
(x0 | f) /* p is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
K7(NAT, the carrier of CNS) is set
K6(K7(NAT, the carrier of CNS)) is set
((x0 | f) /* p) . x1 is Element of the carrier of CNS
(x0 | f) /. (p . x1) is Element of the carrier of CNS
x0 /. (p . x1) is Element of the carrier of CNS
x0 /* p is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
(x0 /* p) . x1 is Element of the carrier of CNS
x0 /. (lim p) is Element of the carrier of CNS
(x0 | f) /. (lim p) is Element of the carrier of CNS
lim (x0 /* p) is Element of the carrier of CNS
p is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
rng p is Element of K6( the carrier of X)
lim p is Element of the carrier of X
x0 /* p is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
x0 /. (lim p) is Element of the carrier of CNS
lim (x0 /* p) is Element of the carrier of CNS
x0 | f is Relation-like the carrier of X -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of X, the carrier of CNS))
dom (x0 | f) is Element of K6( the carrier of X)
(dom x0) /\ f is Element of K6( the carrier of X)
p is Element of the carrier of X
x1 is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
rng x1 is Element of K6( the carrier of X)
lim x1 is Element of the carrier of X
dom x1 is V45() V46() V47() V48() V49() V50() Element of K6(NAT)
x2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
x1 . x2 is Element of the carrier of X
(x0 | f) /* x1 is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
K7(NAT, the carrier of CNS) is set
K6(K7(NAT, the carrier of CNS)) is set
((x0 | f) /* x1) . x2 is Element of the carrier of CNS
(x0 | f) /. (x1 . x2) is Element of the carrier of CNS
x0 /. (x1 . x2) is Element of the carrier of CNS
x0 /* x1 is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
(x0 /* x1) . x2 is Element of the carrier of CNS
(x0 | f) /. (lim x1) is Element of the carrier of CNS
x0 /. (lim x1) is Element of the carrier of CNS
lim ((x0 | f) /* x1) is Element of the carrier of CNS
(x0 | f) /. p is Element of the carrier of CNS
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of X is non empty set
K7( the carrier of CNS, the carrier of X) is set
K6(K7( the carrier of CNS, the carrier of X)) is set
f is set
x0 is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
dom x0 is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
p is Element of the carrier of CNS
x0 /. p is Element of the carrier of X
x1 is V11() real ext-real Element of REAL
x0 | f is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
dom (x0 | f) is Element of K6( the carrier of CNS)
(x0 | f) /. p is Element of the carrier of X
x2 is V11() real ext-real Element of REAL
s9 is Element of the carrier of CNS
s9 - p is Element of the carrier of CNS
||.(s9 - p).|| is V11() real ext-real Element of REAL
x0 /. s9 is Element of the carrier of X
(x0 /. s9) - (x0 /. p) is Element of the carrier of X
||.((x0 /. s9) - (x0 /. p)).|| is V11() real ext-real Element of REAL
(dom x0) /\ f is Element of K6( the carrier of CNS)
(x0 | f) /. s9 is Element of the carrier of X
((x0 | f) /. s9) - (x0 /. p) is Element of the carrier of X
||.(((x0 | f) /. s9) - (x0 /. p)).|| is V11() real ext-real Element of REAL
((x0 | f) /. s9) - ((x0 | f) /. p) is Element of the carrier of X
||.(((x0 | f) /. s9) - ((x0 | f) /. p)).|| is V11() real ext-real Element of REAL
x0 | f is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
dom (x0 | f) is Element of K6( the carrier of CNS)
(dom x0) /\ f is Element of K6( the carrier of CNS)
p is Element of the carrier of CNS
(x0 | f) /. p is Element of the carrier of X
x1 is V11() real ext-real Element of REAL
x0 /. p is Element of the carrier of X
x2 is V11() real ext-real Element of REAL
s9 is Element of the carrier of CNS
s9 - p is Element of the carrier of CNS
||.(s9 - p).|| is V11() real ext-real Element of REAL
(x0 | f) /. s9 is Element of the carrier of X
((x0 | f) /. s9) - ((x0 | f) /. p) is Element of the carrier of X
||.(((x0 | f) /. s9) - ((x0 | f) /. p)).|| is V11() real ext-real Element of REAL
((x0 | f) /. s9) - (x0 /. p) is Element of the carrier of X
||.(((x0 | f) /. s9) - (x0 /. p)).|| is V11() real ext-real Element of REAL
x0 /. s9 is Element of the carrier of X
(x0 /. s9) - (x0 /. p) is Element of the carrier of X
||.((x0 /. s9) - (x0 /. p)).|| is V11() real ext-real Element of REAL
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of X is non empty set
K7( the carrier of CNS, the carrier of X) is set
K6(K7( the carrier of CNS, the carrier of X)) is set
f is set
x0 is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
dom x0 is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
p is Element of the carrier of CNS
x0 /. p is Element of the carrier of X
x1 is V11() real ext-real Element of REAL
x0 | f is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
dom (x0 | f) is Element of K6( the carrier of CNS)
(x0 | f) /. p is Element of the carrier of X
x2 is V11() real ext-real Element of REAL
s9 is Element of the carrier of CNS
s9 - p is Element of the carrier of CNS
||.(s9 - p).|| is V11() real ext-real Element of REAL
x0 /. s9 is Element of the carrier of X
(x0 /. s9) - (x0 /. p) is Element of the carrier of X
||.((x0 /. s9) - (x0 /. p)).|| is V11() real ext-real Element of REAL
(dom x0) /\ f is Element of K6( the carrier of CNS)
(x0 | f) /. s9 is Element of the carrier of X
((x0 | f) /. s9) - (x0 /. p) is Element of the carrier of X
||.(((x0 | f) /. s9) - (x0 /. p)).|| is V11() real ext-real Element of REAL
((x0 | f) /. s9) - ((x0 | f) /. p) is Element of the carrier of X
||.(((x0 | f) /. s9) - ((x0 | f) /. p)).|| is V11() real ext-real Element of REAL
x0 | f is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
dom (x0 | f) is Element of K6( the carrier of CNS)
(dom x0) /\ f is Element of K6( the carrier of CNS)
p is Element of the carrier of CNS
(x0 | f) /. p is Element of the carrier of X
x1 is V11() real ext-real Element of REAL
x0 /. p is Element of the carrier of X
x2 is V11() real ext-real Element of REAL
s9 is Element of the carrier of CNS
s9 - p is Element of the carrier of CNS
||.(s9 - p).|| is V11() real ext-real Element of REAL
(x0 | f) /. s9 is Element of the carrier of X
((x0 | f) /. s9) - ((x0 | f) /. p) is Element of the carrier of X
||.(((x0 | f) /. s9) - ((x0 | f) /. p)).|| is V11() real ext-real Element of REAL
((x0 | f) /. s9) - (x0 /. p) is Element of the carrier of X
||.(((x0 | f) /. s9) - (x0 /. p)).|| is V11() real ext-real Element of REAL
x0 /. s9 is Element of the carrier of X
(x0 /. s9) - (x0 /. p) is Element of the carrier of X
||.((x0 /. s9) - (x0 /. p)).|| is V11() real ext-real Element of REAL
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of X is non empty set
K7( the carrier of X, the carrier of CNS) is set
K6(K7( the carrier of X, the carrier of CNS)) is set
f is set
x0 is Relation-like the carrier of X -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of X, the carrier of CNS))
dom x0 is Element of K6( the carrier of X)
K6( the carrier of X) is set
p is Element of the carrier of X
x0 /. p is Element of the carrier of CNS
x1 is V11() real ext-real Element of REAL
x0 | f is Relation-like the carrier of X -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of X, the carrier of CNS))
dom (x0 | f) is Element of K6( the carrier of X)
(x0 | f) /. p is Element of the carrier of CNS
x2 is V11() real ext-real Element of REAL
s9 is Element of the carrier of X
s9 - p is Element of the carrier of X
||.(s9 - p).|| is V11() real ext-real Element of REAL
x0 /. s9 is Element of the carrier of CNS
(x0 /. s9) - (x0 /. p) is Element of the carrier of CNS
||.((x0 /. s9) - (x0 /. p)).|| is V11() real ext-real Element of REAL
(dom x0) /\ f is Element of K6( the carrier of X)
(x0 | f) /. s9 is Element of the carrier of CNS
((x0 | f) /. s9) - (x0 /. p) is Element of the carrier of CNS
||.(((x0 | f) /. s9) - (x0 /. p)).|| is V11() real ext-real Element of REAL
((x0 | f) /. s9) - ((x0 | f) /. p) is Element of the carrier of CNS
||.(((x0 | f) /. s9) - ((x0 | f) /. p)).|| is V11() real ext-real Element of REAL
x0 | f is Relation-like the carrier of X -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of X, the carrier of CNS))
dom (x0 | f) is Element of K6( the carrier of X)
(dom x0) /\ f is Element of K6( the carrier of X)
p is Element of the carrier of X
(x0 | f) /. p is Element of the carrier of CNS
x1 is V11() real ext-real Element of REAL
x0 /. p is Element of the carrier of CNS
x2 is V11() real ext-real Element of REAL
s9 is Element of the carrier of X
s9 - p is Element of the carrier of X
||.(s9 - p).|| is V11() real ext-real Element of REAL
(x0 | f) /. s9 is Element of the carrier of CNS
((x0 | f) /. s9) - ((x0 | f) /. p) is Element of the carrier of CNS
||.(((x0 | f) /. s9) - ((x0 | f) /. p)).|| is V11() real ext-real Element of REAL
((x0 | f) /. s9) - (x0 /. p) is Element of the carrier of CNS
||.(((x0 | f) /. s9) - (x0 /. p)).|| is V11() real ext-real Element of REAL
x0 /. s9 is Element of the carrier of CNS
(x0 /. s9) - (x0 /. p) is Element of the carrier of CNS
||.((x0 /. s9) - (x0 /. p)).|| is V11() real ext-real Element of REAL
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
K7( the carrier of CNS,COMPLEX) is complex-valued set
K6(K7( the carrier of CNS,COMPLEX)) is set
X is set
f is Relation-like the carrier of CNS -defined COMPLEX -valued Function-like complex-valued Element of K6(K7( the carrier of CNS,COMPLEX))
dom f is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
x0 is Element of the carrier of CNS
f /. x0 is V11() Element of COMPLEX
p is V11() real ext-real Element of REAL
f | X is Relation-like the carrier of CNS -defined COMPLEX -valued Function-like complex-valued Element of K6(K7( the carrier of CNS,COMPLEX))
dom (f | X) is Element of K6( the carrier of CNS)
(f | X) /. x0 is V11() Element of COMPLEX
x1 is V11() real ext-real Element of REAL
x2 is Element of the carrier of CNS
x2 - x0 is Element of the carrier of CNS
||.(x2 - x0).|| is V11() real ext-real Element of REAL
f /. x2 is V11() Element of COMPLEX
(f /. x2) - (f /. x0) is V11() Element of COMPLEX
|.((f /. x2) - (f /. x0)).| is V11() real ext-real Element of REAL
(dom f) /\ X is Element of K6( the carrier of CNS)
(f | X) /. x2 is V11() Element of COMPLEX
((f | X) /. x2) - (f /. x0) is V11() Element of COMPLEX
|.(((f | X) /. x2) - (f /. x0)).| is V11() real ext-real Element of REAL
((f | X) /. x2) - ((f | X) /. x0) is V11() Element of COMPLEX
|.(((f | X) /. x2) - ((f | X) /. x0)).| is V11() real ext-real Element of REAL
f | X is Relation-like the carrier of CNS -defined COMPLEX -valued Function-like complex-valued Element of K6(K7( the carrier of CNS,COMPLEX))
dom (f | X) is Element of K6( the carrier of CNS)
(dom f) /\ X is Element of K6( the carrier of CNS)
x0 is Element of the carrier of CNS
(f | X) /. x0 is V11() Element of COMPLEX
p is V11() real ext-real Element of REAL
f /. x0 is V11() Element of COMPLEX
x1 is V11() real ext-real Element of REAL
x2 is Element of the carrier of CNS
x2 - x0 is Element of the carrier of CNS
||.(x2 - x0).|| is V11() real ext-real Element of REAL
(f | X) /. x2 is V11() Element of COMPLEX
((f | X) /. x2) - ((f | X) /. x0) is V11() Element of COMPLEX
|.(((f | X) /. x2) - ((f | X) /. x0)).| is V11() real ext-real Element of REAL
((f | X) /. x2) - (f /. x0) is V11() Element of COMPLEX
|.(((f | X) /. x2) - (f /. x0)).| is V11() real ext-real Element of REAL
f /. x2 is V11() Element of COMPLEX
(f /. x2) - (f /. x0) is V11() Element of COMPLEX
|.((f /. x2) - (f /. x0)).| is V11() real ext-real Element of REAL
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
K7( the carrier of CNS,REAL) is complex-valued ext-real-valued real-valued set
K6(K7( the carrier of CNS,REAL)) is set
X is set
f is Relation-like the carrier of CNS -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7( the carrier of CNS,REAL))
dom f is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
x0 is Element of the carrier of CNS
f /. x0 is V11() real ext-real Element of REAL
p is V11() real ext-real Element of REAL
f | X is Relation-like the carrier of CNS -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7( the carrier of CNS,REAL))
dom (f | X) is Element of K6( the carrier of CNS)
(f | X) /. x0 is V11() real ext-real Element of REAL
x1 is V11() real ext-real Element of REAL
x2 is Element of the carrier of CNS
x2 - x0 is Element of the carrier of CNS
||.(x2 - x0).|| is V11() real ext-real Element of REAL
f /. x2 is V11() real ext-real Element of REAL
(f /. x2) - (f /. x0) is V11() real ext-real Element of REAL
abs ((f /. x2) - (f /. x0)) is V11() real ext-real Element of REAL
(dom f) /\ X is Element of K6( the carrier of CNS)
(f | X) /. x2 is V11() real ext-real Element of REAL
((f | X) /. x2) - (f /. x0) is V11() real ext-real Element of REAL
abs (((f | X) /. x2) - (f /. x0)) is V11() real ext-real Element of REAL
((f | X) /. x2) - ((f | X) /. x0) is V11() real ext-real Element of REAL
abs (((f | X) /. x2) - ((f | X) /. x0)) is V11() real ext-real Element of REAL
f | X is Relation-like the carrier of CNS -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7( the carrier of CNS,REAL))
dom (f | X) is Element of K6( the carrier of CNS)
(dom f) /\ X is Element of K6( the carrier of CNS)
x0 is Element of the carrier of CNS
(f | X) /. x0 is V11() real ext-real Element of REAL
p is V11() real ext-real Element of REAL
f /. x0 is V11() real ext-real Element of REAL
x1 is V11() real ext-real Element of REAL
x2 is Element of the carrier of CNS
x2 - x0 is Element of the carrier of CNS
||.(x2 - x0).|| is V11() real ext-real Element of REAL
(f | X) /. x2 is V11() real ext-real Element of REAL
((f | X) /. x2) - ((f | X) /. x0) is V11() real ext-real Element of REAL
abs (((f | X) /. x2) - ((f | X) /. x0)) is V11() real ext-real Element of REAL
((f | X) /. x2) - (f /. x0) is V11() real ext-real Element of REAL
abs (((f | X) /. x2) - (f /. x0)) is V11() real ext-real Element of REAL
f /. x2 is V11() real ext-real Element of REAL
(f /. x2) - (f /. x0) is V11() real ext-real Element of REAL
abs ((f /. x2) - (f /. x0)) is V11() real ext-real Element of REAL
CNS is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of CNS is non empty set
K7( the carrier of CNS,COMPLEX) is complex-valued set
K6(K7( the carrier of CNS,COMPLEX)) is set
X is set
f is Relation-like the carrier of CNS -defined COMPLEX -valued Function-like complex-valued Element of K6(K7( the carrier of CNS,COMPLEX))
dom f is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
x0 is Element of the carrier of CNS
f /. x0 is V11() Element of COMPLEX
p is V11() real ext-real Element of REAL
f | X is Relation-like the carrier of CNS -defined COMPLEX -valued Function-like complex-valued Element of K6(K7( the carrier of CNS,COMPLEX))
dom (f | X) is Element of K6( the carrier of CNS)
(f | X) /. x0 is V11() Element of COMPLEX
x1 is V11() real ext-real Element of REAL
x2 is Element of the carrier of CNS
x2 - x0 is Element of the carrier of CNS
||.(x2 - x0).|| is V11() real ext-real Element of REAL
f /. x2 is V11() Element of COMPLEX
(f /. x2) - (f /. x0) is V11() Element of COMPLEX
|.((f /. x2) - (f /. x0)).| is V11() real ext-real Element of REAL
(dom f) /\ X is Element of K6( the carrier of CNS)
(f | X) /. x2 is V11() Element of COMPLEX
((f | X) /. x2) - (f /. x0) is V11() Element of COMPLEX
|.(((f | X) /. x2) - (f /. x0)).| is V11() real ext-real Element of REAL
((f | X) /. x2) - ((f | X) /. x0) is V11() Element of COMPLEX
|.(((f | X) /. x2) - ((f | X) /. x0)).| is V11() real ext-real Element of REAL
f | X is Relation-like the carrier of CNS -defined COMPLEX -valued Function-like complex-valued Element of K6(K7( the carrier of CNS,COMPLEX))
dom (f | X) is Element of K6( the carrier of CNS)
(dom f) /\ X is Element of K6( the carrier of CNS)
x0 is Element of the carrier of CNS
(f | X) /. x0 is V11() Element of COMPLEX
p is V11() real ext-real Element of REAL
f /. x0 is V11() Element of COMPLEX
x1 is V11() real ext-real Element of REAL
x2 is Element of the carrier of CNS
x2 - x0 is Element of the carrier of CNS
||.(x2 - x0).|| is V11() real ext-real Element of REAL
(f | X) /. x2 is V11() Element of COMPLEX
((f | X) /. x2) - ((f | X) /. x0) is V11() Element of COMPLEX
|.(((f | X) /. x2) - ((f | X) /. x0)).| is V11() real ext-real Element of REAL
((f | X) /. x2) - (f /. x0) is V11() Element of COMPLEX
|.(((f | X) /. x2) - (f /. x0)).| is V11() real ext-real Element of REAL
f /. x2 is V11() Element of COMPLEX
(f /. x2) - (f /. x0) is V11() Element of COMPLEX
|.((f /. x2) - (f /. x0)).| is V11() real ext-real Element of REAL
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of X is non empty set
K7( the carrier of CNS, the carrier of X) is set
K6(K7( the carrier of CNS, the carrier of X)) is set
f is set
x0 is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
x0 | f is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
dom x0 is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
(dom x0) /\ f is Element of K6( the carrier of CNS)
dom (x0 | f) is Element of K6( the carrier of CNS)
(x0 | f) | f is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
p is Element of the carrier of CNS
dom (x0 | f) is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
dom x0 is Element of K6( the carrier of CNS)
(dom x0) /\ f is Element of K6( the carrier of CNS)
p is Element of the carrier of CNS
(x0 | f) | f is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of X is non empty set
K7( the carrier of CNS, the carrier of X) is set
K6(K7( the carrier of CNS, the carrier of X)) is set
f is set
x0 is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
x0 | f is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
dom x0 is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
(dom x0) /\ f is Element of K6( the carrier of CNS)
dom (x0 | f) is Element of K6( the carrier of CNS)
(x0 | f) | f is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
p is Element of the carrier of CNS
dom (x0 | f) is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
dom x0 is Element of K6( the carrier of CNS)
(dom x0) /\ f is Element of K6( the carrier of CNS)
p is Element of the carrier of CNS
(x0 | f) | f is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of X is non empty set
K7( the carrier of X, the carrier of CNS) is set
K6(K7( the carrier of X, the carrier of CNS)) is set
f is set
x0 is Relation-like the carrier of X -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of X, the carrier of CNS))
x0 | f is Relation-like the carrier of X -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of X, the carrier of CNS))
dom x0 is Element of K6( the carrier of X)
K6( the carrier of X) is set
(dom x0) /\ f is Element of K6( the carrier of X)
dom (x0 | f) is Element of K6( the carrier of X)
(x0 | f) | f is Relation-like the carrier of X -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of X, the carrier of CNS))
p is Element of the carrier of X
dom (x0 | f) is Element of K6( the carrier of X)
K6( the carrier of X) is set
dom x0 is Element of K6( the carrier of X)
(dom x0) /\ f is Element of K6( the carrier of X)
p is Element of the carrier of X
(x0 | f) | f is Relation-like the carrier of X -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of X, the carrier of CNS))
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
K7( the carrier of CNS,COMPLEX) is complex-valued set
K6(K7( the carrier of CNS,COMPLEX)) is set
X is set
f is Relation-like the carrier of CNS -defined COMPLEX -valued Function-like complex-valued Element of K6(K7( the carrier of CNS,COMPLEX))
f | X is Relation-like the carrier of CNS -defined COMPLEX -valued Function-like complex-valued Element of K6(K7( the carrier of CNS,COMPLEX))
dom f is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
(dom f) /\ X is Element of K6( the carrier of CNS)
dom (f | X) is Element of K6( the carrier of CNS)
(f | X) | X is Relation-like the carrier of CNS -defined COMPLEX -valued Function-like complex-valued Element of K6(K7( the carrier of CNS,COMPLEX))
x0 is Element of the carrier of CNS
dom (f | X) is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
dom f is Element of K6( the carrier of CNS)
(dom f) /\ X is Element of K6( the carrier of CNS)
x0 is Element of the carrier of CNS
(f | X) | X is Relation-like the carrier of CNS -defined COMPLEX -valued Function-like complex-valued Element of K6(K7( the carrier of CNS,COMPLEX))
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
K7( the carrier of CNS,REAL) is complex-valued ext-real-valued real-valued set
K6(K7( the carrier of CNS,REAL)) is set
X is set
f is Relation-like the carrier of CNS -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7( the carrier of CNS,REAL))
f | X is Relation-like the carrier of CNS -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7( the carrier of CNS,REAL))
dom f is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
(dom f) /\ X is Element of K6( the carrier of CNS)
dom (f | X) is Element of K6( the carrier of CNS)
(f | X) | X is Relation-like the carrier of CNS -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7( the carrier of CNS,REAL))
x0 is Element of the carrier of CNS
dom (f | X) is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
dom f is Element of K6( the carrier of CNS)
(dom f) /\ X is Element of K6( the carrier of CNS)
x0 is Element of the carrier of CNS
(f | X) | X is Relation-like the carrier of CNS -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7( the carrier of CNS,REAL))
CNS is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of CNS is non empty set
K7( the carrier of CNS,COMPLEX) is complex-valued set
K6(K7( the carrier of CNS,COMPLEX)) is set
X is set
f is Relation-like the carrier of CNS -defined COMPLEX -valued Function-like complex-valued Element of K6(K7( the carrier of CNS,COMPLEX))
f | X is Relation-like the carrier of CNS -defined COMPLEX -valued Function-like complex-valued Element of K6(K7( the carrier of CNS,COMPLEX))
dom f is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
(dom f) /\ X is Element of K6( the carrier of CNS)
dom (f | X) is Element of K6( the carrier of CNS)
(f | X) | X is Relation-like the carrier of CNS -defined COMPLEX -valued Function-like complex-valued Element of K6(K7( the carrier of CNS,COMPLEX))
x0 is Element of the carrier of CNS
dom (f | X) is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
dom f is Element of K6( the carrier of CNS)
(dom f) /\ X is Element of K6( the carrier of CNS)
x0 is Element of the carrier of CNS
(f | X) | X is Relation-like the carrier of CNS -defined COMPLEX -valued Function-like complex-valued Element of K6(K7( the carrier of CNS,COMPLEX))
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of X is non empty set
K7( the carrier of CNS, the carrier of X) is set
K6(K7( the carrier of CNS, the carrier of X)) is set
f is set
x0 is set
p is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
dom p is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
p | x0 is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
x1 is Element of the carrier of CNS
p | f is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
(dom p) /\ x0 is Element of K6( the carrier of CNS)
(dom p) /\ f is Element of K6( the carrier of CNS)
dom (p | x0) is Element of K6( the carrier of CNS)
dom (p | f) is Element of K6( the carrier of CNS)
K7(NAT, the carrier of CNS) is set
K6(K7(NAT, the carrier of CNS)) is set
(p | x0) /. x1 is Element of the carrier of X
(p | f) /. x1 is Element of the carrier of X
p /. x1 is Element of the carrier of X
x2 is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
rng x2 is Element of K6( the carrier of CNS)
lim x2 is Element of the carrier of CNS
(p | x0) /* x2 is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
K7(NAT, the carrier of X) is set
K6(K7(NAT, the carrier of X)) is set
lim ((p | x0) /* x2) is Element of the carrier of X
dom x2 is V45() V46() V47() V48() V49() V50() Element of K6(NAT)
s9 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
x2 . s9 is Element of the carrier of CNS
(p | f) /* x2 is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
((p | f) /* x2) . s9 is Element of the carrier of X
(p | f) /. (x2 . s9) is Element of the carrier of X
p /. (x2 . s9) is Element of the carrier of X
(p | x0) /. (x2 . s9) is Element of the carrier of X
((p | x0) /* x2) . s9 is Element of the carrier of X
lim ((p | f) /* x2) is Element of the carrier of X
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of X is non empty set
K7( the carrier of CNS, the carrier of X) is set
K6(K7( the carrier of CNS, the carrier of X)) is set
f is set
x0 is set
p is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
dom p is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
p | x0 is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
x1 is Element of the carrier of CNS
p | f is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
(dom p) /\ x0 is Element of K6( the carrier of CNS)
(dom p) /\ f is Element of K6( the carrier of CNS)
dom (p | x0) is Element of K6( the carrier of CNS)
dom (p | f) is Element of K6( the carrier of CNS)
K7(NAT, the carrier of CNS) is set
K6(K7(NAT, the carrier of CNS)) is set
(p | x0) /. x1 is Element of the carrier of X
(p | f) /. x1 is Element of the carrier of X
p /. x1 is Element of the carrier of X
x2 is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
rng x2 is Element of K6( the carrier of CNS)
lim x2 is Element of the carrier of CNS
(p | x0) /* x2 is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
K7(NAT, the carrier of X) is set
K6(K7(NAT, the carrier of X)) is set
lim ((p | x0) /* x2) is Element of the carrier of X
dom x2 is V45() V46() V47() V48() V49() V50() Element of K6(NAT)
s9 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
x2 . s9 is Element of the carrier of CNS
(p | f) /* x2 is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
((p | f) /* x2) . s9 is Element of the carrier of X
(p | f) /. (x2 . s9) is Element of the carrier of X
p /. (x2 . s9) is Element of the carrier of X
(p | x0) /. (x2 . s9) is Element of the carrier of X
((p | x0) /* x2) . s9 is Element of the carrier of X
lim ((p | f) /* x2) is Element of the carrier of X
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of X is non empty set
K7( the carrier of X, the carrier of CNS) is set
K6(K7( the carrier of X, the carrier of CNS)) is set
f is set
x0 is set
p is Relation-like the carrier of X -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of X, the carrier of CNS))
dom p is Element of K6( the carrier of X)
K6( the carrier of X) is set
p | x0 is Relation-like the carrier of X -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of X, the carrier of CNS))
x1 is Element of the carrier of X
p | f is Relation-like the carrier of X -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of X, the carrier of CNS))
(dom p) /\ x0 is Element of K6( the carrier of X)
(dom p) /\ f is Element of K6( the carrier of X)
dom (p | x0) is Element of K6( the carrier of X)
dom (p | f) is Element of K6( the carrier of X)
K7(NAT, the carrier of X) is set
K6(K7(NAT, the carrier of X)) is set
(p | x0) /. x1 is Element of the carrier of CNS
(p | f) /. x1 is Element of the carrier of CNS
p /. x1 is Element of the carrier of CNS
x2 is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
rng x2 is Element of K6( the carrier of X)
lim x2 is Element of the carrier of X
(p | x0) /* x2 is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
K7(NAT, the carrier of CNS) is set
K6(K7(NAT, the carrier of CNS)) is set
lim ((p | x0) /* x2) is Element of the carrier of CNS
dom x2 is V45() V46() V47() V48() V49() V50() Element of K6(NAT)
s9 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
x2 . s9 is Element of the carrier of X
(p | f) /* x2 is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
((p | f) /* x2) . s9 is Element of the carrier of CNS
(p | f) /. (x2 . s9) is Element of the carrier of CNS
p /. (x2 . s9) is Element of the carrier of CNS
(p | x0) /. (x2 . s9) is Element of the carrier of CNS
((p | x0) /* x2) . s9 is Element of the carrier of CNS
lim ((p | f) /* x2) is Element of the carrier of CNS
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of X is non empty set
K7( the carrier of CNS, the carrier of X) is set
K6(K7( the carrier of CNS, the carrier of X)) is set
f is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
dom f is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
x0 is Element of the carrier of CNS
{x0} is non empty set
p is set
f | {x0} is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
p is Element of the carrier of CNS
(dom f) /\ {x0} is Element of K6( the carrier of CNS)
dom (f | {x0}) is Element of K6( the carrier of CNS)
K7(NAT, the carrier of CNS) is set
K6(K7(NAT, the carrier of CNS)) is set
(f | {x0}) /. p is Element of the carrier of X
x1 is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
rng x1 is Element of K6( the carrier of CNS)
lim x1 is Element of the carrier of CNS
(f | {x0}) /* x1 is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
K7(NAT, the carrier of X) is set
K6(K7(NAT, the carrier of X)) is set
lim ((f | {x0}) /* x1) is Element of the carrier of X
dom x1 is V45() V46() V47() V48() V49() V50() Element of K6(NAT)
x2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
x1 . x2 is Element of the carrier of CNS
x2 is V11() real ext-real Element of REAL
s9 is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() V51() Element of NAT
x1 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
((f | {x0}) /* x1) . x1 is Element of the carrier of X
(((f | {x0}) /* x1) . x1) - ((f | {x0}) /. p) is Element of the carrier of X
||.((((f | {x0}) /* x1) . x1) - ((f | {x0}) /. p)).|| is V11() real ext-real Element of REAL
x1 . x1 is Element of the carrier of CNS
(f | {x0}) /. (x1 . x1) is Element of the carrier of X
(f | {x0}) /. x0 is Element of the carrier of X
((f | {x0}) /. (x1 . x1)) - ((f | {x0}) /. x0) is Element of the carrier of X
||.(((f | {x0}) /. (x1 . x1)) - ((f | {x0}) /. x0)).|| is V11() real ext-real Element of REAL
((f | {x0}) /. x0) - ((f | {x0}) /. x0) is Element of the carrier of X
||.(((f | {x0}) /. x0) - ((f | {x0}) /. x0)).|| is V11() real ext-real Element of REAL
0. X is V97(X) Element of the carrier of X
||.(0. X).|| is V11() real ext-real Element of REAL
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of X is non empty set
K7( the carrier of CNS, the carrier of X) is set
K6(K7( the carrier of CNS, the carrier of X)) is set
f is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
dom f is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
x0 is Element of the carrier of CNS
{x0} is non empty set
p is set
f | {x0} is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
p is Element of the carrier of CNS
(dom f) /\ {x0} is Element of K6( the carrier of CNS)
dom (f | {x0}) is Element of K6( the carrier of CNS)
K7(NAT, the carrier of CNS) is set
K6(K7(NAT, the carrier of CNS)) is set
(f | {x0}) /. p is Element of the carrier of X
x1 is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
rng x1 is Element of K6( the carrier of CNS)
lim x1 is Element of the carrier of CNS
(f | {x0}) /* x1 is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
K7(NAT, the carrier of X) is set
K6(K7(NAT, the carrier of X)) is set
lim ((f | {x0}) /* x1) is Element of the carrier of X
dom x1 is V45() V46() V47() V48() V49() V50() Element of K6(NAT)
x2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
x1 . x2 is Element of the carrier of CNS
x2 is V11() real ext-real Element of REAL
s9 is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() V51() Element of NAT
x1 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
((f | {x0}) /* x1) . x1 is Element of the carrier of X
(((f | {x0}) /* x1) . x1) - ((f | {x0}) /. p) is Element of the carrier of X
||.((((f | {x0}) /* x1) . x1) - ((f | {x0}) /. p)).|| is V11() real ext-real Element of REAL
x1 . x1 is Element of the carrier of CNS
(f | {x0}) /. (x1 . x1) is Element of the carrier of X
(f | {x0}) /. x0 is Element of the carrier of X
((f | {x0}) /. (x1 . x1)) - ((f | {x0}) /. x0) is Element of the carrier of X
||.(((f | {x0}) /. (x1 . x1)) - ((f | {x0}) /. x0)).|| is V11() real ext-real Element of REAL
((f | {x0}) /. x0) - ((f | {x0}) /. x0) is Element of the carrier of X
||.(((f | {x0}) /. x0) - ((f | {x0}) /. x0)).|| is V11() real ext-real Element of REAL
0. X is V97(X) Element of the carrier of X
||.(0. X).|| is V11() real ext-real Element of REAL
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of X is non empty set
K7( the carrier of X, the carrier of CNS) is set
K6(K7( the carrier of X, the carrier of CNS)) is set
f is Relation-like the carrier of X -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of X, the carrier of CNS))
dom f is Element of K6( the carrier of X)
K6( the carrier of X) is set
x0 is Element of the carrier of X
{x0} is non empty set
p is set
f | {x0} is Relation-like the carrier of X -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of X, the carrier of CNS))
p is Element of the carrier of X
(dom f) /\ {x0} is Element of K6( the carrier of X)
dom (f | {x0}) is Element of K6( the carrier of X)
K7(NAT, the carrier of X) is set
K6(K7(NAT, the carrier of X)) is set
(f | {x0}) /. p is Element of the carrier of CNS
x1 is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
rng x1 is Element of K6( the carrier of X)
lim x1 is Element of the carrier of X
(f | {x0}) /* x1 is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
K7(NAT, the carrier of CNS) is set
K6(K7(NAT, the carrier of CNS)) is set
lim ((f | {x0}) /* x1) is Element of the carrier of CNS
dom x1 is V45() V46() V47() V48() V49() V50() Element of K6(NAT)
x2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
x1 . x2 is Element of the carrier of X
x2 is V11() real ext-real Element of REAL
s9 is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() V51() Element of NAT
x1 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
((f | {x0}) /* x1) . x1 is Element of the carrier of CNS
(((f | {x0}) /* x1) . x1) - ((f | {x0}) /. p) is Element of the carrier of CNS
||.((((f | {x0}) /* x1) . x1) - ((f | {x0}) /. p)).|| is V11() real ext-real Element of REAL
x1 . x1 is Element of the carrier of X
(f | {x0}) /. (x1 . x1) is Element of the carrier of CNS
(f | {x0}) /. x0 is Element of the carrier of CNS
((f | {x0}) /. (x1 . x1)) - ((f | {x0}) /. x0) is Element of the carrier of CNS
||.(((f | {x0}) /. (x1 . x1)) - ((f | {x0}) /. x0)).|| is V11() real ext-real Element of REAL
((f | {x0}) /. x0) - ((f | {x0}) /. x0) is Element of the carrier of CNS
||.(((f | {x0}) /. x0) - ((f | {x0}) /. x0)).|| is V11() real ext-real Element of REAL
0. CNS is V97(CNS) Element of the carrier of CNS
||.(0. CNS).|| is V11() real ext-real Element of REAL
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of X is non empty set
K7( the carrier of CNS, the carrier of X) is set
K6(K7( the carrier of CNS, the carrier of X)) is set
f is set
x0 is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
p is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
x0 + p is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
x0 - p is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
dom x0 is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
dom p is Element of K6( the carrier of CNS)
(dom x0) /\ (dom p) is Element of K6( the carrier of CNS)
dom (x0 + p) is Element of K6( the carrier of CNS)
K7(NAT, the carrier of CNS) is set
K6(K7(NAT, the carrier of CNS)) is set
x1 is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
rng x1 is Element of K6( the carrier of CNS)
lim x1 is Element of the carrier of CNS
x0 /* x1 is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
K7(NAT, the carrier of X) is set
K6(K7(NAT, the carrier of X)) is set
p /* x1 is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
(x0 /* x1) + (p /* x1) is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
x0 /. (lim x1) is Element of the carrier of X
lim (x0 /* x1) is Element of the carrier of X
p /. (lim x1) is Element of the carrier of X
lim (p /* x1) is Element of the carrier of X
(x0 + p) /. (lim x1) is Element of the carrier of X
(lim (x0 /* x1)) + (lim (p /* x1)) is Element of the carrier of X
lim ((x0 /* x1) + (p /* x1)) is Element of the carrier of X
(x0 + p) /* x1 is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
lim ((x0 + p) /* x1) is Element of the carrier of X
dom (x0 - p) is Element of K6( the carrier of CNS)
x1 is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
rng x1 is Element of K6( the carrier of CNS)
lim x1 is Element of the carrier of CNS
x0 /* x1 is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
p /* x1 is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
(x0 /* x1) - (p /* x1) is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
x0 /. (lim x1) is Element of the carrier of X
lim (x0 /* x1) is Element of the carrier of X
p /. (lim x1) is Element of the carrier of X
lim (p /* x1) is Element of the carrier of X
(x0 - p) /. (lim x1) is Element of the carrier of X
(lim (x0 /* x1)) - (lim (p /* x1)) is Element of the carrier of X
lim ((x0 /* x1) - (p /* x1)) is Element of the carrier of X
(x0 - p) /* x1 is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
lim ((x0 - p) /* x1) is Element of the carrier of X
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of X is non empty set
K7( the carrier of CNS, the carrier of X) is set
K6(K7( the carrier of CNS, the carrier of X)) is set
f is set
x0 is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
p is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
x0 + p is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
x0 - p is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
dom x0 is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
dom p is Element of K6( the carrier of CNS)
(dom x0) /\ (dom p) is Element of K6( the carrier of CNS)
dom (x0 + p) is Element of K6( the carrier of CNS)
K7(NAT, the carrier of CNS) is set
K6(K7(NAT, the carrier of CNS)) is set
x1 is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
rng x1 is Element of K6( the carrier of CNS)
lim x1 is Element of the carrier of CNS
x0 /* x1 is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
K7(NAT, the carrier of X) is set
K6(K7(NAT, the carrier of X)) is set
p /* x1 is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
(x0 /* x1) + (p /* x1) is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
x0 /. (lim x1) is Element of the carrier of X
lim (x0 /* x1) is Element of the carrier of X
p /. (lim x1) is Element of the carrier of X
lim (p /* x1) is Element of the carrier of X
(x0 + p) /. (lim x1) is Element of the carrier of X
(lim (x0 /* x1)) + (lim (p /* x1)) is Element of the carrier of X
lim ((x0 /* x1) + (p /* x1)) is Element of the carrier of X
(x0 + p) /* x1 is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
lim ((x0 + p) /* x1) is Element of the carrier of X
dom (x0 - p) is Element of K6( the carrier of CNS)
x1 is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
rng x1 is Element of K6( the carrier of CNS)
lim x1 is Element of the carrier of CNS
x0 /* x1 is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
p /* x1 is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
(x0 /* x1) - (p /* x1) is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
x0 /. (lim x1) is Element of the carrier of X
lim (x0 /* x1) is Element of the carrier of X
p /. (lim x1) is Element of the carrier of X
lim (p /* x1) is Element of the carrier of X
(x0 - p) /. (lim x1) is Element of the carrier of X
(lim (x0 /* x1)) - (lim (p /* x1)) is Element of the carrier of X
lim ((x0 /* x1) - (p /* x1)) is Element of the carrier of X
(x0 - p) /* x1 is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
lim ((x0 - p) /* x1) is Element of the carrier of X
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of X is non empty set
K7( the carrier of X, the carrier of CNS) is set
K6(K7( the carrier of X, the carrier of CNS)) is set
f is set
x0 is Relation-like the carrier of X -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of X, the carrier of CNS))
p is Relation-like the carrier of X -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of X, the carrier of CNS))
x0 + p is Relation-like the carrier of X -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of X, the carrier of CNS))
x0 - p is Relation-like the carrier of X -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of X, the carrier of CNS))
dom x0 is Element of K6( the carrier of X)
K6( the carrier of X) is set
dom p is Element of K6( the carrier of X)
(dom x0) /\ (dom p) is Element of K6( the carrier of X)
dom (x0 + p) is Element of K6( the carrier of X)
K7(NAT, the carrier of X) is set
K6(K7(NAT, the carrier of X)) is set
x1 is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
rng x1 is Element of K6( the carrier of X)
lim x1 is Element of the carrier of X
x0 /* x1 is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
K7(NAT, the carrier of CNS) is set
K6(K7(NAT, the carrier of CNS)) is set
p /* x1 is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
(x0 /* x1) + (p /* x1) is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
x0 /. (lim x1) is Element of the carrier of CNS
lim (x0 /* x1) is Element of the carrier of CNS
p /. (lim x1) is Element of the carrier of CNS
lim (p /* x1) is Element of the carrier of CNS
(x0 + p) /. (lim x1) is Element of the carrier of CNS
(lim (x0 /* x1)) + (lim (p /* x1)) is Element of the carrier of CNS
lim ((x0 /* x1) + (p /* x1)) is Element of the carrier of CNS
(x0 + p) /* x1 is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
lim ((x0 + p) /* x1) is Element of the carrier of CNS
dom (x0 - p) is Element of K6( the carrier of X)
x1 is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
rng x1 is Element of K6( the carrier of X)
lim x1 is Element of the carrier of X
x0 /* x1 is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
p /* x1 is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
(x0 /* x1) - (p /* x1) is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
x0 /. (lim x1) is Element of the carrier of CNS
lim (x0 /* x1) is Element of the carrier of CNS
p /. (lim x1) is Element of the carrier of CNS
lim (p /* x1) is Element of the carrier of CNS
(x0 - p) /. (lim x1) is Element of the carrier of CNS
(lim (x0 /* x1)) - (lim (p /* x1)) is Element of the carrier of CNS
lim ((x0 /* x1) - (p /* x1)) is Element of the carrier of CNS
(x0 - p) /* x1 is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
lim ((x0 - p) /* x1) is Element of the carrier of CNS
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of X is non empty set
K7( the carrier of CNS, the carrier of X) is set
K6(K7( the carrier of CNS, the carrier of X)) is set
f is set
x0 is set
f /\ x0 is set
p is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
x1 is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
p + x1 is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
p - x1 is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of X is non empty set
K7( the carrier of CNS, the carrier of X) is set
K6(K7( the carrier of CNS, the carrier of X)) is set
f is set
x0 is set
f /\ x0 is set
p is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
x1 is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
p + x1 is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
p - x1 is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of X is non empty set
K7( the carrier of X, the carrier of CNS) is set
K6(K7( the carrier of X, the carrier of CNS)) is set
f is set
x0 is set
f /\ x0 is set
p is Relation-like the carrier of X -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of X, the carrier of CNS))
x1 is Relation-like the carrier of X -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of X, the carrier of CNS))
p + x1 is Relation-like the carrier of X -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of X, the carrier of CNS))
p - x1 is Relation-like the carrier of X -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of X, the carrier of CNS))
CNS is V11() set
X is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of X is non empty set
f is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of f is non empty set
K7( the carrier of X, the carrier of f) is set
K6(K7( the carrier of X, the carrier of f)) is set
x0 is set
p is Relation-like the carrier of X -defined the carrier of f -valued Function-like Element of K6(K7( the carrier of X, the carrier of f))
CNS (#) p is Relation-like the carrier of X -defined the carrier of f -valued Function-like Element of K6(K7( the carrier of X, the carrier of f))
dom p is Element of K6( the carrier of X)
K6( the carrier of X) is set
dom (CNS (#) p) is Element of K6( the carrier of X)
K7(NAT, the carrier of X) is set
K6(K7(NAT, the carrier of X)) is set
x1 is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
rng x1 is Element of K6( the carrier of X)
lim x1 is Element of the carrier of X
p /* x1 is non empty Relation-like NAT -defined the carrier of f -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of f))
K7(NAT, the carrier of f) is set
K6(K7(NAT, the carrier of f)) is set
CNS * (p /* x1) is non empty Relation-like NAT -defined the carrier of f -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of f))
p /. (lim x1) is Element of the carrier of f
lim (p /* x1) is Element of the carrier of f
(CNS (#) p) /. (lim x1) is Element of the carrier of f
CNS * (lim (p /* x1)) is Element of the carrier of f
lim (CNS * (p /* x1)) is Element of the carrier of f
(CNS (#) p) /* x1 is non empty Relation-like NAT -defined the carrier of f -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of f))
lim ((CNS (#) p) /* x1) is Element of the carrier of f
CNS is V11() real ext-real Element of REAL
X is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of X is non empty set
f is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of f is non empty set
K7( the carrier of X, the carrier of f) is set
K6(K7( the carrier of X, the carrier of f)) is set
x0 is set
p is Relation-like the carrier of X -defined the carrier of f -valued Function-like Element of K6(K7( the carrier of X, the carrier of f))
CNS (#) p is Relation-like the carrier of X -defined the carrier of f -valued Function-like Element of K6(K7( the carrier of X, the carrier of f))
dom p is Element of K6( the carrier of X)
K6( the carrier of X) is set
dom (CNS (#) p) is Element of K6( the carrier of X)
K7(NAT, the carrier of X) is set
K6(K7(NAT, the carrier of X)) is set
x1 is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
rng x1 is Element of K6( the carrier of X)
lim x1 is Element of the carrier of X
p /* x1 is non empty Relation-like NAT -defined the carrier of f -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of f))
K7(NAT, the carrier of f) is set
K6(K7(NAT, the carrier of f)) is set
CNS * (p /* x1) is non empty Relation-like NAT -defined the carrier of f -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of f))
p /. (lim x1) is Element of the carrier of f
lim (p /* x1) is Element of the carrier of f
(CNS (#) p) /. (lim x1) is Element of the carrier of f
CNS * (lim (p /* x1)) is Element of the carrier of f
lim (CNS * (p /* x1)) is Element of the carrier of f
(CNS (#) p) /* x1 is non empty Relation-like NAT -defined the carrier of f -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of f))
lim ((CNS (#) p) /* x1) is Element of the carrier of f
CNS is V11() set
X is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of X is non empty set
f is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of f is non empty set
K7( the carrier of f, the carrier of X) is set
K6(K7( the carrier of f, the carrier of X)) is set
x0 is set
p is Relation-like the carrier of f -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of f, the carrier of X))
CNS (#) p is Relation-like the carrier of f -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of f, the carrier of X))
dom p is Element of K6( the carrier of f)
K6( the carrier of f) is set
dom (CNS (#) p) is Element of K6( the carrier of f)
K7(NAT, the carrier of f) is set
K6(K7(NAT, the carrier of f)) is set
x1 is non empty Relation-like NAT -defined the carrier of f -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of f))
rng x1 is Element of K6( the carrier of f)
lim x1 is Element of the carrier of f
p /* x1 is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
K7(NAT, the carrier of X) is set
K6(K7(NAT, the carrier of X)) is set
CNS * (p /* x1) is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
p /. (lim x1) is Element of the carrier of X
lim (p /* x1) is Element of the carrier of X
(CNS (#) p) /. (lim x1) is Element of the carrier of X
CNS * (lim (p /* x1)) is Element of the carrier of X
lim (CNS * (p /* x1)) is Element of the carrier of X
(CNS (#) p) /* x1 is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
lim ((CNS (#) p) /* x1) is Element of the carrier of X
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of X is non empty set
K7( the carrier of CNS, the carrier of X) is set
K6(K7( the carrier of CNS, the carrier of X)) is set
f is set
x0 is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
||.x0.|| is Relation-like the carrier of CNS -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7( the carrier of CNS,REAL))
K7( the carrier of CNS,REAL) is complex-valued ext-real-valued real-valued set
K6(K7( the carrier of CNS,REAL)) is set
- x0 is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
dom x0 is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
dom ||.x0.|| is Element of K6( the carrier of CNS)
||.x0.|| | f is Relation-like the carrier of CNS -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7( the carrier of CNS,REAL))
p is Element of the carrier of CNS
x0 | f is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
(dom ||.x0.||) /\ f is Element of K6( the carrier of CNS)
dom (||.x0.|| | f) is Element of K6( the carrier of CNS)
K7(NAT, the carrier of CNS) is set
K6(K7(NAT, the carrier of CNS)) is set
(||.x0.|| | f) /. p is V11() real ext-real Element of REAL
x1 is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
rng x1 is Element of K6( the carrier of CNS)
lim x1 is Element of the carrier of CNS
(||.x0.|| | f) /* x1 is non empty Relation-like NAT -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
lim ((||.x0.|| | f) /* x1) is V11() real ext-real Element of REAL
(dom x0) /\ f is Element of K6( the carrier of CNS)
dom (x0 | f) is Element of K6( the carrier of CNS)
(x0 | f) /. p is Element of the carrier of X
(x0 | f) /* x1 is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
K7(NAT, the carrier of X) is set
K6(K7(NAT, the carrier of X)) is set
lim ((x0 | f) /* x1) is Element of the carrier of X
dom x1 is V45() V46() V47() V48() V49() V50() Element of K6(NAT)
x2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
x1 . x2 is Element of the carrier of CNS
||.((x0 | f) /* x1).|| is non empty Relation-like NAT -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
||.((x0 | f) /* x1).|| . x2 is V11() real ext-real Element of REAL
((x0 | f) /* x1) . x2 is Element of the carrier of X
||.(((x0 | f) /* x1) . x2).|| is V11() real ext-real Element of REAL
(x0 | f) /. (x1 . x2) is Element of the carrier of X
||.((x0 | f) /. (x1 . x2)).|| is V11() real ext-real Element of REAL
x0 /. (x1 . x2) is Element of the carrier of X
||.(x0 /. (x1 . x2)).|| is V11() real ext-real Element of REAL
||.x0.|| . (x1 . x2) is V11() real ext-real Element of REAL
(||.x0.|| | f) . (x1 . x2) is V11() real ext-real Element of REAL
(||.x0.|| | f) /. (x1 . x2) is V11() real ext-real Element of REAL
((||.x0.|| | f) /* x1) . x2 is V11() real ext-real Element of REAL
||.((x0 | f) /. p).|| is V11() real ext-real Element of REAL
x0 /. p is Element of the carrier of X
||.(x0 /. p).|| is V11() real ext-real Element of REAL
||.x0.|| . p is V11() real ext-real Element of REAL
||.x0.|| /. p is V11() real ext-real Element of REAL
(- 1r) (#) x0 is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of X is non empty set
K7( the carrier of CNS, the carrier of X) is set
K6(K7( the carrier of CNS, the carrier of X)) is set
f is set
x0 is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
||.x0.|| is Relation-like the carrier of CNS -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7( the carrier of CNS,REAL))
K7( the carrier of CNS,REAL) is complex-valued ext-real-valued real-valued set
K6(K7( the carrier of CNS,REAL)) is set
- x0 is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
dom x0 is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
dom ||.x0.|| is Element of K6( the carrier of CNS)
||.x0.|| | f is Relation-like the carrier of CNS -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7( the carrier of CNS,REAL))
p is Element of the carrier of CNS
x0 | f is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
(dom ||.x0.||) /\ f is Element of K6( the carrier of CNS)
dom (||.x0.|| | f) is Element of K6( the carrier of CNS)
K7(NAT, the carrier of CNS) is set
K6(K7(NAT, the carrier of CNS)) is set
(||.x0.|| | f) /. p is V11() real ext-real Element of REAL
x1 is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
rng x1 is Element of K6( the carrier of CNS)
lim x1 is Element of the carrier of CNS
(||.x0.|| | f) /* x1 is non empty Relation-like NAT -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
lim ((||.x0.|| | f) /* x1) is V11() real ext-real Element of REAL
(dom x0) /\ f is Element of K6( the carrier of CNS)
dom (x0 | f) is Element of K6( the carrier of CNS)
(x0 | f) /. p is Element of the carrier of X
(x0 | f) /* x1 is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
K7(NAT, the carrier of X) is set
K6(K7(NAT, the carrier of X)) is set
lim ((x0 | f) /* x1) is Element of the carrier of X
dom x1 is V45() V46() V47() V48() V49() V50() Element of K6(NAT)
x2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
x1 . x2 is Element of the carrier of CNS
||.((x0 | f) /* x1).|| is non empty Relation-like NAT -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
||.((x0 | f) /* x1).|| . x2 is V11() real ext-real Element of REAL
((x0 | f) /* x1) . x2 is Element of the carrier of X
||.(((x0 | f) /* x1) . x2).|| is V11() real ext-real Element of REAL
(x0 | f) /. (x1 . x2) is Element of the carrier of X
||.((x0 | f) /. (x1 . x2)).|| is V11() real ext-real Element of REAL
x0 /. (x1 . x2) is Element of the carrier of X
||.(x0 /. (x1 . x2)).|| is V11() real ext-real Element of REAL
||.x0.|| . (x1 . x2) is V11() real ext-real Element of REAL
(||.x0.|| | f) . (x1 . x2) is V11() real ext-real Element of REAL
(||.x0.|| | f) /. (x1 . x2) is V11() real ext-real Element of REAL
((||.x0.|| | f) /* x1) . x2 is V11() real ext-real Element of REAL
||.((x0 | f) /. p).|| is V11() real ext-real Element of REAL
x0 /. p is Element of the carrier of X
||.(x0 /. p).|| is V11() real ext-real Element of REAL
||.x0.|| . p is V11() real ext-real Element of REAL
||.x0.|| /. p is V11() real ext-real Element of REAL
(- 1) (#) x0 is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of X is non empty set
K7( the carrier of X, the carrier of CNS) is set
K6(K7( the carrier of X, the carrier of CNS)) is set
f is set
x0 is Relation-like the carrier of X -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of X, the carrier of CNS))
||.x0.|| is Relation-like the carrier of X -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7( the carrier of X,REAL))
K7( the carrier of X,REAL) is complex-valued ext-real-valued real-valued set
K6(K7( the carrier of X,REAL)) is set
- x0 is Relation-like the carrier of X -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of X, the carrier of CNS))
dom x0 is Element of K6( the carrier of X)
K6( the carrier of X) is set
dom ||.x0.|| is Element of K6( the carrier of X)
||.x0.|| | f is Relation-like the carrier of X -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7( the carrier of X,REAL))
p is Element of the carrier of X
x0 | f is Relation-like the carrier of X -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of X, the carrier of CNS))
(dom ||.x0.||) /\ f is Element of K6( the carrier of X)
dom (||.x0.|| | f) is Element of K6( the carrier of X)
K7(NAT, the carrier of X) is set
K6(K7(NAT, the carrier of X)) is set
(||.x0.|| | f) /. p is V11() real ext-real Element of REAL
x1 is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
rng x1 is Element of K6( the carrier of X)
lim x1 is Element of the carrier of X
(||.x0.|| | f) /* x1 is non empty Relation-like NAT -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
lim ((||.x0.|| | f) /* x1) is V11() real ext-real Element of REAL
(dom x0) /\ f is Element of K6( the carrier of X)
dom (x0 | f) is Element of K6( the carrier of X)
(x0 | f) /. p is Element of the carrier of CNS
(x0 | f) /* x1 is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
K7(NAT, the carrier of CNS) is set
K6(K7(NAT, the carrier of CNS)) is set
lim ((x0 | f) /* x1) is Element of the carrier of CNS
dom x1 is V45() V46() V47() V48() V49() V50() Element of K6(NAT)
x2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
x1 . x2 is Element of the carrier of X
||.((x0 | f) /* x1).|| is non empty Relation-like NAT -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
||.((x0 | f) /* x1).|| . x2 is V11() real ext-real Element of REAL
((x0 | f) /* x1) . x2 is Element of the carrier of CNS
||.(((x0 | f) /* x1) . x2).|| is V11() real ext-real Element of REAL
(x0 | f) /. (x1 . x2) is Element of the carrier of CNS
||.((x0 | f) /. (x1 . x2)).|| is V11() real ext-real Element of REAL
x0 /. (x1 . x2) is Element of the carrier of CNS
||.(x0 /. (x1 . x2)).|| is V11() real ext-real Element of REAL
||.x0.|| . (x1 . x2) is V11() real ext-real Element of REAL
(||.x0.|| | f) . (x1 . x2) is V11() real ext-real Element of REAL
(||.x0.|| | f) /. (x1 . x2) is V11() real ext-real Element of REAL
((||.x0.|| | f) /* x1) . x2 is V11() real ext-real Element of REAL
||.((x0 | f) /. p).|| is V11() real ext-real Element of REAL
x0 /. p is Element of the carrier of CNS
||.(x0 /. p).|| is V11() real ext-real Element of REAL
||.x0.|| . p is V11() real ext-real Element of REAL
||.x0.|| /. p is V11() real ext-real Element of REAL
(- 1r) (#) x0 is Relation-like the carrier of X -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of X, the carrier of CNS))
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of X is non empty set
K7( the carrier of CNS, the carrier of X) is set
K6(K7( the carrier of CNS, the carrier of X)) is set
f is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
dom f is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
x0 is Element of the carrier of CNS
f /. x0 is Element of the carrier of X
0. X is V97(X) Element of the carrier of X
(f /. x0) + (0. X) is Element of the carrier of X
0. CNS is V97(CNS) Element of the carrier of CNS
x0 + (0. CNS) is Element of the carrier of CNS
f /. (x0 + (0. CNS)) is Element of the carrier of X
f /. (0. CNS) is Element of the carrier of X
(f /. x0) + (f /. (0. CNS)) is Element of the carrier of X
p is Element of the carrier of CNS
- p is Element of the carrier of CNS
p + (- p) is Element of the carrier of CNS
f /. (p + (- p)) is Element of the carrier of X
f /. p is Element of the carrier of X
f /. (- p) is Element of the carrier of X
(f /. p) + (f /. (- p)) is Element of the carrier of X
- (f /. p) is Element of the carrier of X
p is Element of the carrier of CNS
x1 is Element of the carrier of CNS
p - x1 is Element of the carrier of CNS
f /. (p - x1) is Element of the carrier of X
- x1 is Element of the carrier of CNS
p + (- x1) is Element of the carrier of CNS
f /. (p + (- x1)) is Element of the carrier of X
f /. p is Element of the carrier of X
f /. (- x1) is Element of the carrier of X
(f /. p) + (f /. (- x1)) is Element of the carrier of X
f /. x1 is Element of the carrier of X
- (f /. x1) is Element of the carrier of X
(f /. p) + (- (f /. x1)) is Element of the carrier of X
(f /. p) - (f /. x1) is Element of the carrier of X
p is Element of the carrier of CNS
x1 is V11() real ext-real Element of REAL
p - x0 is Element of the carrier of CNS
s9 is V11() real ext-real Element of REAL
x1 is V11() real ext-real Element of REAL
x1 is Element of the carrier of CNS
x1 - p is Element of the carrier of CNS
||.(x1 - p).|| is V11() real ext-real Element of REAL
(p - x0) + x0 is Element of the carrier of CNS
x0 - x0 is Element of the carrier of CNS
p - (x0 - x0) is Element of the carrier of CNS
p - (0. CNS) is Element of the carrier of CNS
x1 - (p - x0) is Element of the carrier of CNS
(x1 - (p - x0)) - x0 is Element of the carrier of CNS
||.((x1 - (p - x0)) - x0).|| is V11() real ext-real Element of REAL
f /. x1 is Element of the carrier of X
f /. p is Element of the carrier of X
(f /. x1) - (f /. p) is Element of the carrier of X
||.((f /. x1) - (f /. p)).|| is V11() real ext-real Element of REAL
f /. (p - x0) is Element of the carrier of X
(f /. (p - x0)) + (f /. x0) is Element of the carrier of X
(f /. x1) - ((f /. (p - x0)) + (f /. x0)) is Element of the carrier of X
||.((f /. x1) - ((f /. (p - x0)) + (f /. x0))).|| is V11() real ext-real Element of REAL
(f /. x1) - (f /. (p - x0)) is Element of the carrier of X
((f /. x1) - (f /. (p - x0))) - (f /. x0) is Element of the carrier of X
||.(((f /. x1) - (f /. (p - x0))) - (f /. x0)).|| is V11() real ext-real Element of REAL
f /. (x1 - (p - x0)) is Element of the carrier of X
(f /. (x1 - (p - x0))) - (f /. x0) is Element of the carrier of X
||.((f /. (x1 - (p - x0))) - (f /. x0)).|| is V11() real ext-real Element of REAL
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of X is non empty set
K7( the carrier of CNS, the carrier of X) is set
K6(K7( the carrier of CNS, the carrier of X)) is set
f is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
dom f is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
x0 is Element of the carrier of CNS
f /. x0 is Element of the carrier of X
0. X is V97(X) Element of the carrier of X
(f /. x0) + (0. X) is Element of the carrier of X
0. CNS is V97(CNS) Element of the carrier of CNS
x0 + (0. CNS) is Element of the carrier of CNS
f /. (x0 + (0. CNS)) is Element of the carrier of X
f /. (0. CNS) is Element of the carrier of X
(f /. x0) + (f /. (0. CNS)) is Element of the carrier of X
p is Element of the carrier of CNS
- p is Element of the carrier of CNS
p + (- p) is Element of the carrier of CNS
f /. (p + (- p)) is Element of the carrier of X
f /. p is Element of the carrier of X
f /. (- p) is Element of the carrier of X
(f /. p) + (f /. (- p)) is Element of the carrier of X
- (f /. p) is Element of the carrier of X
p is Element of the carrier of CNS
x1 is Element of the carrier of CNS
p - x1 is Element of the carrier of CNS
f /. (p - x1) is Element of the carrier of X
- x1 is Element of the carrier of CNS
p + (- x1) is Element of the carrier of CNS
f /. (p + (- x1)) is Element of the carrier of X
f /. p is Element of the carrier of X
f /. (- x1) is Element of the carrier of X
(f /. p) + (f /. (- x1)) is Element of the carrier of X
f /. x1 is Element of the carrier of X
- (f /. x1) is Element of the carrier of X
(f /. p) + (- (f /. x1)) is Element of the carrier of X
(f /. p) - (f /. x1) is Element of the carrier of X
p is Element of the carrier of CNS
x1 is V11() real ext-real Element of REAL
p - x0 is Element of the carrier of CNS
s9 is V11() real ext-real Element of REAL
x1 is V11() real ext-real Element of REAL
x1 is Element of the carrier of CNS
x1 - p is Element of the carrier of CNS
||.(x1 - p).|| is V11() real ext-real Element of REAL
(p - x0) + x0 is Element of the carrier of CNS
x0 - x0 is Element of the carrier of CNS
p - (x0 - x0) is Element of the carrier of CNS
p - (0. CNS) is Element of the carrier of CNS
x1 - (p - x0) is Element of the carrier of CNS
(x1 - (p - x0)) - x0 is Element of the carrier of CNS
||.((x1 - (p - x0)) - x0).|| is V11() real ext-real Element of REAL
f /. x1 is Element of the carrier of X
f /. p is Element of the carrier of X
(f /. x1) - (f /. p) is Element of the carrier of X
||.((f /. x1) - (f /. p)).|| is V11() real ext-real Element of REAL
f /. (p - x0) is Element of the carrier of X
(f /. (p - x0)) + (f /. x0) is Element of the carrier of X
(f /. x1) - ((f /. (p - x0)) + (f /. x0)) is Element of the carrier of X
||.((f /. x1) - ((f /. (p - x0)) + (f /. x0))).|| is V11() real ext-real Element of REAL
(f /. x1) - (f /. (p - x0)) is Element of the carrier of X
((f /. x1) - (f /. (p - x0))) - (f /. x0) is Element of the carrier of X
||.(((f /. x1) - (f /. (p - x0))) - (f /. x0)).|| is V11() real ext-real Element of REAL
f /. (x1 - (p - x0)) is Element of the carrier of X
(f /. (x1 - (p - x0))) - (f /. x0) is Element of the carrier of X
||.((f /. (x1 - (p - x0))) - (f /. x0)).|| is V11() real ext-real Element of REAL
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of X is non empty set
K7( the carrier of X, the carrier of CNS) is set
K6(K7( the carrier of X, the carrier of CNS)) is set
f is Relation-like the carrier of X -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of X, the carrier of CNS))
dom f is Element of K6( the carrier of X)
K6( the carrier of X) is set
x0 is Element of the carrier of X
f /. x0 is Element of the carrier of CNS
0. CNS is V97(CNS) Element of the carrier of CNS
(f /. x0) + (0. CNS) is Element of the carrier of CNS
0. X is V97(X) Element of the carrier of X
x0 + (0. X) is Element of the carrier of X
f /. (x0 + (0. X)) is Element of the carrier of CNS
f /. (0. X) is Element of the carrier of CNS
(f /. x0) + (f /. (0. X)) is Element of the carrier of CNS
p is Element of the carrier of X
- p is Element of the carrier of X
p + (- p) is Element of the carrier of X
f /. (p + (- p)) is Element of the carrier of CNS
f /. p is Element of the carrier of CNS
f /. (- p) is Element of the carrier of CNS
(f /. p) + (f /. (- p)) is Element of the carrier of CNS
- (f /. p) is Element of the carrier of CNS
p is Element of the carrier of X
x1 is Element of the carrier of X
p - x1 is Element of the carrier of X
f /. (p - x1) is Element of the carrier of CNS
- x1 is Element of the carrier of X
p + (- x1) is Element of the carrier of X
f /. (p + (- x1)) is Element of the carrier of CNS
f /. p is Element of the carrier of CNS
f /. (- x1) is Element of the carrier of CNS
(f /. p) + (f /. (- x1)) is Element of the carrier of CNS
f /. x1 is Element of the carrier of CNS
- (f /. x1) is Element of the carrier of CNS
(f /. p) + (- (f /. x1)) is Element of the carrier of CNS
(f /. p) - (f /. x1) is Element of the carrier of CNS
p is Element of the carrier of X
x1 is V11() real ext-real Element of REAL
p - x0 is Element of the carrier of X
s9 is V11() real ext-real Element of REAL
x1 is V11() real ext-real Element of REAL
x1 is Element of the carrier of X
x1 - p is Element of the carrier of X
||.(x1 - p).|| is V11() real ext-real Element of REAL
(p - x0) + x0 is Element of the carrier of X
x0 - x0 is Element of the carrier of X
p - (x0 - x0) is Element of the carrier of X
p - (0. X) is Element of the carrier of X
x1 - (p - x0) is Element of the carrier of X
(x1 - (p - x0)) - x0 is Element of the carrier of X
||.((x1 - (p - x0)) - x0).|| is V11() real ext-real Element of REAL
f /. x1 is Element of the carrier of CNS
f /. p is Element of the carrier of CNS
(f /. x1) - (f /. p) is Element of the carrier of CNS
||.((f /. x1) - (f /. p)).|| is V11() real ext-real Element of REAL
f /. (p - x0) is Element of the carrier of CNS
(f /. (p - x0)) + (f /. x0) is Element of the carrier of CNS
(f /. x1) - ((f /. (p - x0)) + (f /. x0)) is Element of the carrier of CNS
||.((f /. x1) - ((f /. (p - x0)) + (f /. x0))).|| is V11() real ext-real Element of REAL
(f /. x1) - (f /. (p - x0)) is Element of the carrier of CNS
((f /. x1) - (f /. (p - x0))) - (f /. x0) is Element of the carrier of CNS
||.(((f /. x1) - (f /. (p - x0))) - (f /. x0)).|| is V11() real ext-real Element of REAL
f /. (x1 - (p - x0)) is Element of the carrier of CNS
(f /. (x1 - (p - x0))) - (f /. x0) is Element of the carrier of CNS
||.((f /. (x1 - (p - x0))) - (f /. x0)).|| is V11() real ext-real Element of REAL
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of X is non empty set
K7( the carrier of CNS, the carrier of X) is set
K6(K7( the carrier of CNS, the carrier of X)) is set
f is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
dom f is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
rng f is Element of K6( the carrier of X)
K6( the carrier of X) is set
K7(NAT, the carrier of X) is set
K6(K7(NAT, the carrier of X)) is set
x0 is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
rng x0 is Element of K6( the carrier of X)
p is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
x0 . p is set
dom x0 is V45() V46() V47() V48() V49() V50() Element of K6(NAT)
x0 . p is Element of the carrier of X
x1 is Element of the carrier of CNS
f . x1 is set
f /. x1 is Element of the carrier of X
K7(NAT, the carrier of CNS) is set
K6(K7(NAT, the carrier of CNS)) is set
p is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
x1 is set
rng p is Element of K6( the carrier of CNS)
x2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
p . x2 is Element of the carrier of CNS
x1 is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
lim x1 is Element of the carrier of CNS
f /* x1 is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
rng x1 is Element of K6( the carrier of CNS)
s9 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
p . s9 is Element of the carrier of CNS
f /. (p . s9) is Element of the carrier of X
x0 . s9 is Element of the carrier of X
f /* p is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
(f /* p) . s9 is Element of the carrier of X
f | (dom f) is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
f /. (lim x1) is Element of the carrier of X
lim (f /* x1) is Element of the carrier of X
x2 is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
lim x2 is Element of the carrier of X
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of X is non empty set
K7( the carrier of CNS, the carrier of X) is set
K6(K7( the carrier of CNS, the carrier of X)) is set
f is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
dom f is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
rng f is Element of K6( the carrier of X)
K6( the carrier of X) is set
K7(NAT, the carrier of X) is set
K6(K7(NAT, the carrier of X)) is set
x0 is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
rng x0 is Element of K6( the carrier of X)
p is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
x0 . p is set
dom x0 is V45() V46() V47() V48() V49() V50() Element of K6(NAT)
x0 . p is Element of the carrier of X
x1 is Element of the carrier of CNS
f . x1 is set
f /. x1 is Element of the carrier of X
K7(NAT, the carrier of CNS) is set
K6(K7(NAT, the carrier of CNS)) is set
p is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
x1 is set
rng p is Element of K6( the carrier of CNS)
x2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
p . x2 is Element of the carrier of CNS
x1 is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
lim x1 is Element of the carrier of CNS
f /* x1 is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
rng x1 is Element of K6( the carrier of CNS)
s9 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
p . s9 is Element of the carrier of CNS
f /. (p . s9) is Element of the carrier of X
x0 . s9 is Element of the carrier of X
f /* p is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
(f /* p) . s9 is Element of the carrier of X
f | (dom f) is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
f /. (lim x1) is Element of the carrier of X
lim (f /* x1) is Element of the carrier of X
x2 is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
lim x2 is Element of the carrier of X
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of X is non empty set
K7( the carrier of X, the carrier of CNS) is set
K6(K7( the carrier of X, the carrier of CNS)) is set
f is Relation-like the carrier of X -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of X, the carrier of CNS))
dom f is Element of K6( the carrier of X)
K6( the carrier of X) is set
rng f is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
K7(NAT, the carrier of CNS) is set
K6(K7(NAT, the carrier of CNS)) is set
x0 is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
rng x0 is Element of K6( the carrier of CNS)
p is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
x0 . p is set
dom x0 is V45() V46() V47() V48() V49() V50() Element of K6(NAT)
x0 . p is Element of the carrier of CNS
x1 is Element of the carrier of X
f . x1 is set
f /. x1 is Element of the carrier of CNS
K7(NAT, the carrier of X) is set
K6(K7(NAT, the carrier of X)) is set
p is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
x1 is set
rng p is Element of K6( the carrier of X)
x2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
p . x2 is Element of the carrier of X
x1 is non empty Relation-like NAT -defined the carrier of X -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of X))
lim x1 is Element of the carrier of X
f /* x1 is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
rng x1 is Element of K6( the carrier of X)
s9 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
p . s9 is Element of the carrier of X
f /. (p . s9) is Element of the carrier of CNS
x0 . s9 is Element of the carrier of CNS
f /* p is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
(f /* p) . s9 is Element of the carrier of CNS
f | (dom f) is Relation-like the carrier of X -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of X, the carrier of CNS))
f /. (lim x1) is Element of the carrier of CNS
lim (f /* x1) is Element of the carrier of CNS
x2 is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
lim x2 is Element of the carrier of CNS
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
K7( the carrier of CNS,COMPLEX) is complex-valued set
K6(K7( the carrier of CNS,COMPLEX)) is set
X is Relation-like the carrier of CNS -defined COMPLEX -valued Function-like complex-valued Element of K6(K7( the carrier of CNS,COMPLEX))
dom X is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
rng X is V45() Element of K6(COMPLEX)
K6(COMPLEX) is set
f is non empty Relation-like NAT -defined COMPLEX -valued Function-like total quasi_total complex-valued Element of K6(K7(NAT,COMPLEX))
rng f is V45() Element of K6(COMPLEX)
x0 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
f . x0 is V11() set
dom f is V45() V46() V47() V48() V49() V50() Element of K6(NAT)
f . x0 is V11() Element of COMPLEX
p is Element of the carrier of CNS
X . p is V11() set
X /. p is V11() Element of COMPLEX
K7(NAT, the carrier of CNS) is set
K6(K7(NAT, the carrier of CNS)) is set
x0 is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
p is set
rng x0 is Element of K6( the carrier of CNS)
x1 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
x0 . x1 is Element of the carrier of CNS
p is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
lim p is Element of the carrier of CNS
X /* p is non empty Relation-like NAT -defined COMPLEX -valued Function-like total quasi_total complex-valued Element of K6(K7(NAT,COMPLEX))
rng p is Element of K6( the carrier of CNS)
x2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
x0 . x2 is Element of the carrier of CNS
X /. (x0 . x2) is V11() Element of COMPLEX
f . x2 is V11() Element of COMPLEX
X /* x0 is non empty Relation-like NAT -defined COMPLEX -valued Function-like total quasi_total complex-valued Element of K6(K7(NAT,COMPLEX))
(X /* x0) . x2 is V11() Element of COMPLEX
X | (dom X) is Relation-like the carrier of CNS -defined COMPLEX -valued Function-like complex-valued Element of K6(K7( the carrier of CNS,COMPLEX))
X /. (lim p) is V11() Element of COMPLEX
lim (X /* p) is V11() Element of COMPLEX
x1 is non empty Relation-like NAT -defined COMPLEX -valued Function-like total quasi_total complex-valued Element of K6(K7(NAT,COMPLEX))
lim x1 is V11() Element of COMPLEX
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
K7( the carrier of CNS,REAL) is complex-valued ext-real-valued real-valued set
K6(K7( the carrier of CNS,REAL)) is set
X is Relation-like the carrier of CNS -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7( the carrier of CNS,REAL))
dom X is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
rng X is V45() V46() V47() Element of K6(REAL)
f is non empty Relation-like NAT -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
rng f is V45() V46() V47() Element of K6(REAL)
x0 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
f . x0 is V11() real ext-real Element of REAL
dom f is V45() V46() V47() V48() V49() V50() Element of K6(NAT)
p is Element of the carrier of CNS
X . p is V11() real ext-real Element of REAL
X /. p is V11() real ext-real Element of REAL
K7(NAT, the carrier of CNS) is set
K6(K7(NAT, the carrier of CNS)) is set
x0 is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
p is set
rng x0 is Element of K6( the carrier of CNS)
x1 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
x0 . x1 is Element of the carrier of CNS
p is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
lim p is Element of the carrier of CNS
X /* p is non empty Relation-like NAT -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
rng p is Element of K6( the carrier of CNS)
x2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
x0 . x2 is Element of the carrier of CNS
X /. (x0 . x2) is V11() real ext-real Element of REAL
f . x2 is V11() real ext-real Element of REAL
X /* x0 is non empty Relation-like NAT -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(X /* x0) . x2 is V11() real ext-real Element of REAL
X | (dom X) is Relation-like the carrier of CNS -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7( the carrier of CNS,REAL))
X /. (lim p) is V11() real ext-real Element of REAL
lim (X /* p) is V11() real ext-real Element of REAL
x1 is non empty Relation-like NAT -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
lim x1 is V11() real ext-real Element of REAL
CNS is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of CNS is non empty set
K7( the carrier of CNS,COMPLEX) is complex-valued set
K6(K7( the carrier of CNS,COMPLEX)) is set
X is Relation-like the carrier of CNS -defined COMPLEX -valued Function-like complex-valued Element of K6(K7( the carrier of CNS,COMPLEX))
dom X is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
rng X is V45() Element of K6(COMPLEX)
K6(COMPLEX) is set
f is non empty Relation-like NAT -defined COMPLEX -valued Function-like total quasi_total complex-valued Element of K6(K7(NAT,COMPLEX))
rng f is V45() Element of K6(COMPLEX)
x0 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
f . x0 is V11() set
dom f is V45() V46() V47() V48() V49() V50() Element of K6(NAT)
f . x0 is V11() Element of COMPLEX
p is Element of the carrier of CNS
X . p is V11() set
X /. p is V11() Element of COMPLEX
K7(NAT, the carrier of CNS) is set
K6(K7(NAT, the carrier of CNS)) is set
x0 is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
p is set
rng x0 is Element of K6( the carrier of CNS)
x1 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
x0 . x1 is Element of the carrier of CNS
p is non empty Relation-like NAT -defined the carrier of CNS -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of CNS))
lim p is Element of the carrier of CNS
X /* p is non empty Relation-like NAT -defined COMPLEX -valued Function-like total quasi_total complex-valued Element of K6(K7(NAT,COMPLEX))
rng p is Element of K6( the carrier of CNS)
x2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
x0 . x2 is Element of the carrier of CNS
X /. (x0 . x2) is V11() Element of COMPLEX
f . x2 is V11() Element of COMPLEX
X /* x0 is non empty Relation-like NAT -defined COMPLEX -valued Function-like total quasi_total complex-valued Element of K6(K7(NAT,COMPLEX))
(X /* x0) . x2 is V11() Element of COMPLEX
X | (dom X) is Relation-like the carrier of CNS -defined COMPLEX -valued Function-like complex-valued Element of K6(K7( the carrier of CNS,COMPLEX))
X /. (lim p) is V11() Element of COMPLEX
lim (X /* p) is V11() Element of COMPLEX
x1 is non empty Relation-like NAT -defined COMPLEX -valued Function-like total quasi_total complex-valued Element of K6(K7(NAT,COMPLEX))
lim x1 is V11() Element of COMPLEX
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
K6( the carrier of CNS) is set
X is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of X is non empty set
K7( the carrier of CNS, the carrier of X) is set
K6(K7( the carrier of CNS, the carrier of X)) is set
f is Element of K6( the carrier of CNS)
x0 is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
dom x0 is Element of K6( the carrier of CNS)
x0 .: f is Element of K6( the carrier of X)
K6( the carrier of X) is set
x0 | f is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
dom (x0 | f) is Element of K6( the carrier of CNS)
(dom x0) /\ f is Element of K6( the carrier of CNS)
(x0 | f) | f is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
p is Element of the carrier of CNS
rng (x0 | f) is Element of K6( the carrier of X)
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
K6( the carrier of CNS) is set
X is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of X is non empty set
K7( the carrier of CNS, the carrier of X) is set
K6(K7( the carrier of CNS, the carrier of X)) is set
f is Element of K6( the carrier of CNS)
x0 is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
dom x0 is Element of K6( the carrier of CNS)
x0 .: f is Element of K6( the carrier of X)
K6( the carrier of X) is set
x0 | f is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
dom (x0 | f) is Element of K6( the carrier of CNS)
(dom x0) /\ f is Element of K6( the carrier of CNS)
(x0 | f) | f is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
p is Element of the carrier of CNS
rng (x0 | f) is Element of K6( the carrier of X)
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of X is non empty set
K6( the carrier of X) is set
K7( the carrier of X, the carrier of CNS) is set
K6(K7( the carrier of X, the carrier of CNS)) is set
f is Element of K6( the carrier of X)
x0 is Relation-like the carrier of X -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of X, the carrier of CNS))
dom x0 is Element of K6( the carrier of X)
x0 .: f is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
x0 | f is Relation-like the carrier of X -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of X, the carrier of CNS))
dom (x0 | f) is Element of K6( the carrier of X)
(dom x0) /\ f is Element of K6( the carrier of X)
(x0 | f) | f is Relation-like the carrier of X -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of X, the carrier of CNS))
p is Element of the carrier of X
rng (x0 | f) is Element of K6( the carrier of CNS)
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
K7( the carrier of CNS,REAL) is complex-valued ext-real-valued real-valued set
K6(K7( the carrier of CNS,REAL)) is set
X is Relation-like the carrier of CNS -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7( the carrier of CNS,REAL))
dom X is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
rng X is V45() V46() V47() Element of K6(REAL)
upper_bound (rng X) is V11() real ext-real Element of REAL
lower_bound (rng X) is V11() real ext-real Element of REAL
f is Element of the carrier of CNS
X . f is V11() real ext-real Element of REAL
X /. f is V11() real ext-real Element of REAL
x0 is Element of the carrier of CNS
X . x0 is V11() real ext-real Element of REAL
X /. x0 is V11() real ext-real Element of REAL
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of X is non empty set
K7( the carrier of CNS, the carrier of X) is set
K6(K7( the carrier of CNS, the carrier of X)) is set
f is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
dom f is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
||.f.|| is Relation-like the carrier of CNS -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7( the carrier of CNS,REAL))
K7( the carrier of CNS,REAL) is complex-valued ext-real-valued real-valued set
K6(K7( the carrier of CNS,REAL)) is set
rng ||.f.|| is V45() V46() V47() Element of K6(REAL)
upper_bound (rng ||.f.||) is V11() real ext-real Element of REAL
lower_bound (rng ||.f.||) is V11() real ext-real Element of REAL
dom ||.f.|| is Element of K6( the carrier of CNS)
x0 is Element of the carrier of CNS
||.f.|| . x0 is V11() real ext-real Element of REAL
p is Element of the carrier of CNS
||.f.|| . p is V11() real ext-real Element of REAL
||.f.|| /. x0 is V11() real ext-real Element of REAL
||.f.|| /. p is V11() real ext-real Element of REAL
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of X is non empty set
K7( the carrier of CNS, the carrier of X) is set
K6(K7( the carrier of CNS, the carrier of X)) is set
f is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
dom f is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
||.f.|| is Relation-like the carrier of CNS -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7( the carrier of CNS,REAL))
K7( the carrier of CNS,REAL) is complex-valued ext-real-valued real-valued set
K6(K7( the carrier of CNS,REAL)) is set
rng ||.f.|| is V45() V46() V47() Element of K6(REAL)
upper_bound (rng ||.f.||) is V11() real ext-real Element of REAL
lower_bound (rng ||.f.||) is V11() real ext-real Element of REAL
dom ||.f.|| is Element of K6( the carrier of CNS)
x0 is Element of the carrier of CNS
||.f.|| . x0 is V11() real ext-real Element of REAL
p is Element of the carrier of CNS
||.f.|| . p is V11() real ext-real Element of REAL
||.f.|| /. x0 is V11() real ext-real Element of REAL
||.f.|| /. p is V11() real ext-real Element of REAL
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of X is non empty set
K7( the carrier of X, the carrier of CNS) is set
K6(K7( the carrier of X, the carrier of CNS)) is set
f is Relation-like the carrier of X -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of X, the carrier of CNS))
dom f is Element of K6( the carrier of X)
K6( the carrier of X) is set
||.f.|| is Relation-like the carrier of X -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7( the carrier of X,REAL))
K7( the carrier of X,REAL) is complex-valued ext-real-valued real-valued set
K6(K7( the carrier of X,REAL)) is set
rng ||.f.|| is V45() V46() V47() Element of K6(REAL)
upper_bound (rng ||.f.||) is V11() real ext-real Element of REAL
lower_bound (rng ||.f.||) is V11() real ext-real Element of REAL
dom ||.f.|| is Element of K6( the carrier of X)
x0 is Element of the carrier of X
||.f.|| . x0 is V11() real ext-real Element of REAL
p is Element of the carrier of X
||.f.|| . p is V11() real ext-real Element of REAL
||.f.|| /. x0 is V11() real ext-real Element of REAL
||.f.|| /. p is V11() real ext-real Element of REAL
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of X is non empty set
K7( the carrier of CNS, the carrier of X) is set
K6(K7( the carrier of CNS, the carrier of X)) is set
f is set
x0 is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
||.x0.|| is Relation-like the carrier of CNS -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7( the carrier of CNS,REAL))
K7( the carrier of CNS,REAL) is complex-valued ext-real-valued real-valued set
K6(K7( the carrier of CNS,REAL)) is set
||.x0.|| | f is Relation-like the carrier of CNS -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7( the carrier of CNS,REAL))
x0 | f is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
||.(x0 | f).|| is Relation-like the carrier of CNS -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7( the carrier of CNS,REAL))
dom (||.x0.|| | f) is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
dom ||.x0.|| is Element of K6( the carrier of CNS)
(dom ||.x0.||) /\ f is Element of K6( the carrier of CNS)
dom x0 is Element of K6( the carrier of CNS)
(dom x0) /\ f is Element of K6( the carrier of CNS)
dom (x0 | f) is Element of K6( the carrier of CNS)
dom ||.(x0 | f).|| is Element of K6( the carrier of CNS)
p is Element of the carrier of CNS
(||.x0.|| | f) . p is V11() real ext-real Element of REAL
||.x0.|| . p is V11() real ext-real Element of REAL
x0 /. p is Element of the carrier of X
||.(x0 /. p).|| is V11() real ext-real Element of REAL
(x0 | f) /. p is Element of the carrier of X
||.((x0 | f) /. p).|| is V11() real ext-real Element of REAL
||.(x0 | f).|| . p is V11() real ext-real Element of REAL
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of X is non empty set
K7( the carrier of CNS, the carrier of X) is set
K6(K7( the carrier of CNS, the carrier of X)) is set
f is set
x0 is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
||.x0.|| is Relation-like the carrier of CNS -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7( the carrier of CNS,REAL))
K7( the carrier of CNS,REAL) is complex-valued ext-real-valued real-valued set
K6(K7( the carrier of CNS,REAL)) is set
||.x0.|| | f is Relation-like the carrier of CNS -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7( the carrier of CNS,REAL))
x0 | f is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
||.(x0 | f).|| is Relation-like the carrier of CNS -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7( the carrier of CNS,REAL))
dom (||.x0.|| | f) is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
dom ||.x0.|| is Element of K6( the carrier of CNS)
(dom ||.x0.||) /\ f is Element of K6( the carrier of CNS)
dom x0 is Element of K6( the carrier of CNS)
(dom x0) /\ f is Element of K6( the carrier of CNS)
dom (x0 | f) is Element of K6( the carrier of CNS)
dom ||.(x0 | f).|| is Element of K6( the carrier of CNS)
p is Element of the carrier of CNS
(||.x0.|| | f) . p is V11() real ext-real Element of REAL
||.x0.|| . p is V11() real ext-real Element of REAL
x0 /. p is Element of the carrier of X
||.(x0 /. p).|| is V11() real ext-real Element of REAL
(x0 | f) /. p is Element of the carrier of X
||.((x0 | f) /. p).|| is V11() real ext-real Element of REAL
||.(x0 | f).|| . p is V11() real ext-real Element of REAL
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of X is non empty set
K7( the carrier of X, the carrier of CNS) is set
K6(K7( the carrier of X, the carrier of CNS)) is set
f is set
x0 is Relation-like the carrier of X -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of X, the carrier of CNS))
||.x0.|| is Relation-like the carrier of X -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7( the carrier of X,REAL))
K7( the carrier of X,REAL) is complex-valued ext-real-valued real-valued set
K6(K7( the carrier of X,REAL)) is set
||.x0.|| | f is Relation-like the carrier of X -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7( the carrier of X,REAL))
x0 | f is Relation-like the carrier of X -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of X, the carrier of CNS))
||.(x0 | f).|| is Relation-like the carrier of X -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7( the carrier of X,REAL))
dom (||.x0.|| | f) is Element of K6( the carrier of X)
K6( the carrier of X) is set
dom ||.x0.|| is Element of K6( the carrier of X)
(dom ||.x0.||) /\ f is Element of K6( the carrier of X)
dom x0 is Element of K6( the carrier of X)
(dom x0) /\ f is Element of K6( the carrier of X)
dom (x0 | f) is Element of K6( the carrier of X)
dom ||.(x0 | f).|| is Element of K6( the carrier of X)
p is Element of the carrier of X
(||.x0.|| | f) . p is V11() real ext-real Element of REAL
||.x0.|| . p is V11() real ext-real Element of REAL
x0 /. p is Element of the carrier of CNS
||.(x0 /. p).|| is V11() real ext-real Element of REAL
(x0 | f) /. p is Element of the carrier of CNS
||.((x0 | f) /. p).|| is V11() real ext-real Element of REAL
||.(x0 | f).|| . p is V11() real ext-real Element of REAL
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
K6( the carrier of CNS) is set
X is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of X is non empty set
K7( the carrier of CNS, the carrier of X) is set
K6(K7( the carrier of CNS, the carrier of X)) is set
f is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
dom f is Element of K6( the carrier of CNS)
||.f.|| is Relation-like the carrier of CNS -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7( the carrier of CNS,REAL))
K7( the carrier of CNS,REAL) is complex-valued ext-real-valued real-valued set
K6(K7( the carrier of CNS,REAL)) is set
x0 is Element of K6( the carrier of CNS)
||.f.|| .: x0 is V45() V46() V47() Element of K6(REAL)
upper_bound (||.f.|| .: x0) is V11() real ext-real Element of REAL
lower_bound (||.f.|| .: x0) is V11() real ext-real Element of REAL
f | x0 is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
dom (f | x0) is Element of K6( the carrier of CNS)
(dom f) /\ x0 is Element of K6( the carrier of CNS)
(f | x0) | x0 is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
p is Element of the carrier of CNS
||.(f | x0).|| is Relation-like the carrier of CNS -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7( the carrier of CNS,REAL))
rng ||.(f | x0).|| is V45() V46() V47() Element of K6(REAL)
upper_bound (rng ||.(f | x0).||) is V11() real ext-real Element of REAL
lower_bound (rng ||.(f | x0).||) is V11() real ext-real Element of REAL
p is Element of the carrier of CNS
x1 is Element of the carrier of CNS
||.(f | x0).|| /. p is V11() real ext-real Element of REAL
||.(f | x0).|| /. x1 is V11() real ext-real Element of REAL
dom ||.f.|| is Element of K6( the carrier of CNS)
||.f.|| /. p is V11() real ext-real Element of REAL
||.f.|| /. x1 is V11() real ext-real Element of REAL
||.f.|| | x0 is Relation-like the carrier of CNS -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7( the carrier of CNS,REAL))
rng (||.f.|| | x0) is V45() V46() V47() Element of K6(REAL)
dom ||.(f | x0).|| is Element of K6( the carrier of CNS)
||.(f | x0).|| . x1 is V11() real ext-real Element of REAL
(f | x0) /. x1 is Element of the carrier of X
||.((f | x0) /. x1).|| is V11() real ext-real Element of REAL
f /. x1 is Element of the carrier of X
||.(f /. x1).|| is V11() real ext-real Element of REAL
||.f.|| . x1 is V11() real ext-real Element of REAL
||.(f | x0).|| . p is V11() real ext-real Element of REAL
(f | x0) /. p is Element of the carrier of X
||.((f | x0) /. p).|| is V11() real ext-real Element of REAL
f /. p is Element of the carrier of X
||.(f /. p).|| is V11() real ext-real Element of REAL
||.f.|| . p is V11() real ext-real Element of REAL
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
K6( the carrier of CNS) is set
X is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of X is non empty set
K7( the carrier of CNS, the carrier of X) is set
K6(K7( the carrier of CNS, the carrier of X)) is set
f is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
dom f is Element of K6( the carrier of CNS)
||.f.|| is Relation-like the carrier of CNS -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7( the carrier of CNS,REAL))
K7( the carrier of CNS,REAL) is complex-valued ext-real-valued real-valued set
K6(K7( the carrier of CNS,REAL)) is set
x0 is Element of K6( the carrier of CNS)
||.f.|| .: x0 is V45() V46() V47() Element of K6(REAL)
upper_bound (||.f.|| .: x0) is V11() real ext-real Element of REAL
lower_bound (||.f.|| .: x0) is V11() real ext-real Element of REAL
f | x0 is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
dom (f | x0) is Element of K6( the carrier of CNS)
(dom f) /\ x0 is Element of K6( the carrier of CNS)
(f | x0) | x0 is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
p is Element of the carrier of CNS
||.(f | x0).|| is Relation-like the carrier of CNS -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7( the carrier of CNS,REAL))
rng ||.(f | x0).|| is V45() V46() V47() Element of K6(REAL)
upper_bound (rng ||.(f | x0).||) is V11() real ext-real Element of REAL
lower_bound (rng ||.(f | x0).||) is V11() real ext-real Element of REAL
p is Element of the carrier of CNS
x1 is Element of the carrier of CNS
||.(f | x0).|| /. p is V11() real ext-real Element of REAL
||.(f | x0).|| /. x1 is V11() real ext-real Element of REAL
dom ||.f.|| is Element of K6( the carrier of CNS)
||.f.|| /. p is V11() real ext-real Element of REAL
||.f.|| /. x1 is V11() real ext-real Element of REAL
||.f.|| | x0 is Relation-like the carrier of CNS -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7( the carrier of CNS,REAL))
rng (||.f.|| | x0) is V45() V46() V47() Element of K6(REAL)
dom ||.(f | x0).|| is Element of K6( the carrier of CNS)
||.(f | x0).|| . x1 is V11() real ext-real Element of REAL
(f | x0) /. x1 is Element of the carrier of X
||.((f | x0) /. x1).|| is V11() real ext-real Element of REAL
f /. x1 is Element of the carrier of X
||.(f /. x1).|| is V11() real ext-real Element of REAL
||.f.|| . x1 is V11() real ext-real Element of REAL
||.(f | x0).|| . p is V11() real ext-real Element of REAL
(f | x0) /. p is Element of the carrier of X
||.((f | x0) /. p).|| is V11() real ext-real Element of REAL
f /. p is Element of the carrier of X
||.(f /. p).|| is V11() real ext-real Element of REAL
||.f.|| . p is V11() real ext-real Element of REAL
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of X is non empty set
K7( the carrier of X, the carrier of CNS) is set
K6(K7( the carrier of X, the carrier of CNS)) is set
K6( the carrier of X) is set
f is Relation-like the carrier of X -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of X, the carrier of CNS))
dom f is Element of K6( the carrier of X)
||.f.|| is Relation-like the carrier of X -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7( the carrier of X,REAL))
K7( the carrier of X,REAL) is complex-valued ext-real-valued real-valued set
K6(K7( the carrier of X,REAL)) is set
x0 is Element of K6( the carrier of X)
||.f.|| .: x0 is V45() V46() V47() Element of K6(REAL)
upper_bound (||.f.|| .: x0) is V11() real ext-real Element of REAL
lower_bound (||.f.|| .: x0) is V11() real ext-real Element of REAL
f | x0 is Relation-like the carrier of X -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of X, the carrier of CNS))
dom (f | x0) is Element of K6( the carrier of X)
(dom f) /\ x0 is Element of K6( the carrier of X)
(f | x0) | x0 is Relation-like the carrier of X -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of X, the carrier of CNS))
p is Element of the carrier of X
||.(f | x0).|| is Relation-like the carrier of X -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7( the carrier of X,REAL))
rng ||.(f | x0).|| is V45() V46() V47() Element of K6(REAL)
upper_bound (rng ||.(f | x0).||) is V11() real ext-real Element of REAL
lower_bound (rng ||.(f | x0).||) is V11() real ext-real Element of REAL
p is Element of the carrier of X
x1 is Element of the carrier of X
||.(f | x0).|| /. p is V11() real ext-real Element of REAL
||.(f | x0).|| /. x1 is V11() real ext-real Element of REAL
dom ||.f.|| is Element of K6( the carrier of X)
||.f.|| /. p is V11() real ext-real Element of REAL
||.f.|| /. x1 is V11() real ext-real Element of REAL
||.f.|| | x0 is Relation-like the carrier of X -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7( the carrier of X,REAL))
rng (||.f.|| | x0) is V45() V46() V47() Element of K6(REAL)
dom ||.(f | x0).|| is Element of K6( the carrier of X)
||.(f | x0).|| . x1 is V11() real ext-real Element of REAL
(f | x0) /. x1 is Element of the carrier of CNS
||.((f | x0) /. x1).|| is V11() real ext-real Element of REAL
f /. x1 is Element of the carrier of CNS
||.(f /. x1).|| is V11() real ext-real Element of REAL
||.f.|| . x1 is V11() real ext-real Element of REAL
||.(f | x0).|| . p is V11() real ext-real Element of REAL
(f | x0) /. p is Element of the carrier of CNS
||.((f | x0) /. p).|| is V11() real ext-real Element of REAL
f /. p is Element of the carrier of CNS
||.(f /. p).|| is V11() real ext-real Element of REAL
||.f.|| . p is V11() real ext-real Element of REAL
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
K7( the carrier of CNS,REAL) is complex-valued ext-real-valued real-valued set
K6(K7( the carrier of CNS,REAL)) is set
K6( the carrier of CNS) is set
X is Relation-like the carrier of CNS -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7( the carrier of CNS,REAL))
dom X is Element of K6( the carrier of CNS)
f is Element of K6( the carrier of CNS)
X .: f is V45() V46() V47() Element of K6(REAL)
upper_bound (X .: f) is V11() real ext-real Element of REAL
lower_bound (X .: f) is V11() real ext-real Element of REAL
X | f is Relation-like the carrier of CNS -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7( the carrier of CNS,REAL))
dom (X | f) is Element of K6( the carrier of CNS)
(dom X) /\ f is Element of K6( the carrier of CNS)
(X | f) | f is Relation-like the carrier of CNS -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7( the carrier of CNS,REAL))
x0 is Element of the carrier of CNS
rng (X | f) is V45() V46() V47() Element of K6(REAL)
upper_bound (rng (X | f)) is V11() real ext-real Element of REAL
lower_bound (rng (X | f)) is V11() real ext-real Element of REAL
x0 is Element of the carrier of CNS
p is Element of the carrier of CNS
(X | f) /. x0 is V11() real ext-real Element of REAL
(X | f) /. p is V11() real ext-real Element of REAL
X /. x0 is V11() real ext-real Element of REAL
X /. p is V11() real ext-real Element of REAL
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of X is non empty set
K7( the carrier of CNS, the carrier of X) is set
K6(K7( the carrier of CNS, the carrier of X)) is set
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of X is non empty set
K7( the carrier of CNS, the carrier of X) is set
K6(K7( the carrier of CNS, the carrier of X)) is set
CNS is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of X is non empty set
K7( the carrier of CNS, the carrier of X) is set
K6(K7( the carrier of CNS, the carrier of X)) is set
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
K7( the carrier of CNS,COMPLEX) is complex-valued set
K6(K7( the carrier of CNS,COMPLEX)) is set
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
K7( the carrier of CNS,REAL) is complex-valued ext-real-valued real-valued set
K6(K7( the carrier of CNS,REAL)) is set
CNS is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of CNS is non empty set
K7( the carrier of CNS,COMPLEX) is complex-valued set
K6(K7( the carrier of CNS,COMPLEX)) is set
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of X is non empty set
K7( the carrier of CNS, the carrier of X) is set
K6(K7( the carrier of CNS, the carrier of X)) is set
f is set
x0 is set
p is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
dom p is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
x1 is V11() real ext-real Element of REAL
x2 is Element of the carrier of CNS
s9 is Element of the carrier of CNS
p /. x2 is Element of the carrier of X
p /. s9 is Element of the carrier of X
(p /. x2) - (p /. s9) is Element of the carrier of X
||.((p /. x2) - (p /. s9)).|| is V11() real ext-real Element of REAL
x2 - s9 is Element of the carrier of CNS
||.(x2 - s9).|| is V11() real ext-real Element of REAL
x1 * ||.(x2 - s9).|| is V11() real ext-real Element of REAL
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of X is non empty set
K7( the carrier of CNS, the carrier of X) is set
K6(K7( the carrier of CNS, the carrier of X)) is set
f is set
x0 is set
p is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
dom p is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
x1 is V11() real ext-real Element of REAL
x2 is Element of the carrier of CNS
s9 is Element of the carrier of CNS
p /. x2 is Element of the carrier of X
p /. s9 is Element of the carrier of X
(p /. x2) - (p /. s9) is Element of the carrier of X
||.((p /. x2) - (p /. s9)).|| is V11() real ext-real Element of REAL
x2 - s9 is Element of the carrier of CNS
||.(x2 - s9).|| is V11() real ext-real Element of REAL
x1 * ||.(x2 - s9).|| is V11() real ext-real Element of REAL
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of X is non empty set
K7( the carrier of X, the carrier of CNS) is set
K6(K7( the carrier of X, the carrier of CNS)) is set
f is set
x0 is set
p is Relation-like the carrier of X -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of X, the carrier of CNS))
dom p is Element of K6( the carrier of X)
K6( the carrier of X) is set
x1 is V11() real ext-real Element of REAL
x2 is Element of the carrier of X
s9 is Element of the carrier of X
p /. x2 is Element of the carrier of CNS
p /. s9 is Element of the carrier of CNS
(p /. x2) - (p /. s9) is Element of the carrier of CNS
||.((p /. x2) - (p /. s9)).|| is V11() real ext-real Element of REAL
x2 - s9 is Element of the carrier of X
||.(x2 - s9).|| is V11() real ext-real Element of REAL
x1 * ||.(x2 - s9).|| is V11() real ext-real Element of REAL
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of X is non empty set
K7( the carrier of CNS, the carrier of X) is set
K6(K7( the carrier of CNS, the carrier of X)) is set
f is set
x0 is set
f /\ x0 is set
p is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
x1 is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
p + x1 is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
x2 is V11() real ext-real Element of REAL
dom x1 is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
dom p is Element of K6( the carrier of CNS)
(dom p) /\ (dom x1) is Element of K6( the carrier of CNS)
dom (p + x1) is Element of K6( the carrier of CNS)
s9 is V11() real ext-real Element of REAL
x2 + s9 is V11() real ext-real Element of REAL
x1 is V11() real ext-real Element of REAL
0 + 0 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative Element of REAL
x1 is Element of the carrier of CNS
x2 is Element of the carrier of CNS
(p + x1) /. x1 is Element of the carrier of X
(p + x1) /. x2 is Element of the carrier of X
((p + x1) /. x1) - ((p + x1) /. x2) is Element of the carrier of X
||.(((p + x1) /. x1) - ((p + x1) /. x2)).|| is V11() real ext-real Element of REAL
x1 - x2 is Element of the carrier of CNS
||.(x1 - x2).|| is V11() real ext-real Element of REAL
x1 * ||.(x1 - x2).|| is V11() real ext-real Element of REAL
x1 /. x1 is Element of the carrier of X
x1 /. x2 is Element of the carrier of X
(x1 /. x1) - (x1 /. x2) is Element of the carrier of X
||.((x1 /. x1) - (x1 /. x2)).|| is V11() real ext-real Element of REAL
s9 * ||.(x1 - x2).|| is V11() real ext-real Element of REAL
p /. x1 is Element of the carrier of X
p /. x2 is Element of the carrier of X
(p /. x1) - (p /. x2) is Element of the carrier of X
||.((p /. x1) - (p /. x2)).|| is V11() real ext-real Element of REAL
x2 * ||.(x1 - x2).|| is V11() real ext-real Element of REAL
||.((p /. x1) - (p /. x2)).|| + ||.((x1 /. x1) - (x1 /. x2)).|| is V11() real ext-real Element of REAL
(x2 * ||.(x1 - x2).||) + (s9 * ||.(x1 - x2).||) is V11() real ext-real Element of REAL
(p /. x1) + (x1 /. x1) is Element of the carrier of X
((p /. x1) + (x1 /. x1)) - ((p + x1) /. x2) is Element of the carrier of X
||.(((p /. x1) + (x1 /. x1)) - ((p + x1) /. x2)).|| is V11() real ext-real Element of REAL
(p /. x2) + (x1 /. x2) is Element of the carrier of X
((p /. x1) + (x1 /. x1)) - ((p /. x2) + (x1 /. x2)) is Element of the carrier of X
||.(((p /. x1) + (x1 /. x1)) - ((p /. x2) + (x1 /. x2))).|| is V11() real ext-real Element of REAL
(x1 /. x1) - ((p /. x2) + (x1 /. x2)) is Element of the carrier of X
(p /. x1) + ((x1 /. x1) - ((p /. x2) + (x1 /. x2))) is Element of the carrier of X
||.((p /. x1) + ((x1 /. x1) - ((p /. x2) + (x1 /. x2)))).|| is V11() real ext-real Element of REAL
(x1 /. x1) - (p /. x2) is Element of the carrier of X
((x1 /. x1) - (p /. x2)) - (x1 /. x2) is Element of the carrier of X
(p /. x1) + (((x1 /. x1) - (p /. x2)) - (x1 /. x2)) is Element of the carrier of X
||.((p /. x1) + (((x1 /. x1) - (p /. x2)) - (x1 /. x2))).|| is V11() real ext-real Element of REAL
- (p /. x2) is Element of the carrier of X
(- (p /. x2)) + (x1 /. x1) is Element of the carrier of X
((- (p /. x2)) + (x1 /. x1)) - (x1 /. x2) is Element of the carrier of X
(p /. x1) + (((- (p /. x2)) + (x1 /. x1)) - (x1 /. x2)) is Element of the carrier of X
||.((p /. x1) + (((- (p /. x2)) + (x1 /. x1)) - (x1 /. x2))).|| is V11() real ext-real Element of REAL
(- (p /. x2)) + ((x1 /. x1) - (x1 /. x2)) is Element of the carrier of X
(p /. x1) + ((- (p /. x2)) + ((x1 /. x1) - (x1 /. x2))) is Element of the carrier of X
||.((p /. x1) + ((- (p /. x2)) + ((x1 /. x1) - (x1 /. x2)))).|| is V11() real ext-real Element of REAL
(p /. x1) + (- (p /. x2)) is Element of the carrier of X
((p /. x1) + (- (p /. x2))) + ((x1 /. x1) - (x1 /. x2)) is Element of the carrier of X
||.(((p /. x1) + (- (p /. x2))) + ((x1 /. x1) - (x1 /. x2))).|| is V11() real ext-real Element of REAL
((p /. x1) - (p /. x2)) + ((x1 /. x1) - (x1 /. x2)) is Element of the carrier of X
||.(((p /. x1) - (p /. x2)) + ((x1 /. x1) - (x1 /. x2))).|| is V11() real ext-real Element of REAL
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of X is non empty set
K7( the carrier of CNS, the carrier of X) is set
K6(K7( the carrier of CNS, the carrier of X)) is set
f is set
x0 is set
f /\ x0 is set
p is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
x1 is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
p + x1 is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
x2 is V11() real ext-real Element of REAL
dom x1 is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
dom p is Element of K6( the carrier of CNS)
(dom p) /\ (dom x1) is Element of K6( the carrier of CNS)
dom (p + x1) is Element of K6( the carrier of CNS)
s9 is V11() real ext-real Element of REAL
x2 + s9 is V11() real ext-real Element of REAL
x1 is V11() real ext-real Element of REAL
0 + 0 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative Element of REAL
x1 is Element of the carrier of CNS
x2 is Element of the carrier of CNS
(p + x1) /. x1 is Element of the carrier of X
(p + x1) /. x2 is Element of the carrier of X
((p + x1) /. x1) - ((p + x1) /. x2) is Element of the carrier of X
||.(((p + x1) /. x1) - ((p + x1) /. x2)).|| is V11() real ext-real Element of REAL
x1 - x2 is Element of the carrier of CNS
||.(x1 - x2).|| is V11() real ext-real Element of REAL
x1 * ||.(x1 - x2).|| is V11() real ext-real Element of REAL
x1 /. x1 is Element of the carrier of X
x1 /. x2 is Element of the carrier of X
(x1 /. x1) - (x1 /. x2) is Element of the carrier of X
||.((x1 /. x1) - (x1 /. x2)).|| is V11() real ext-real Element of REAL
s9 * ||.(x1 - x2).|| is V11() real ext-real Element of REAL
p /. x1 is Element of the carrier of X
p /. x2 is Element of the carrier of X
(p /. x1) - (p /. x2) is Element of the carrier of X
||.((p /. x1) - (p /. x2)).|| is V11() real ext-real Element of REAL
x2 * ||.(x1 - x2).|| is V11() real ext-real Element of REAL
||.((p /. x1) - (p /. x2)).|| + ||.((x1 /. x1) - (x1 /. x2)).|| is V11() real ext-real Element of REAL
(x2 * ||.(x1 - x2).||) + (s9 * ||.(x1 - x2).||) is V11() real ext-real Element of REAL
(p /. x1) + (x1 /. x1) is Element of the carrier of X
((p /. x1) + (x1 /. x1)) - ((p + x1) /. x2) is Element of the carrier of X
||.(((p /. x1) + (x1 /. x1)) - ((p + x1) /. x2)).|| is V11() real ext-real Element of REAL
(p /. x2) + (x1 /. x2) is Element of the carrier of X
((p /. x1) + (x1 /. x1)) - ((p /. x2) + (x1 /. x2)) is Element of the carrier of X
||.(((p /. x1) + (x1 /. x1)) - ((p /. x2) + (x1 /. x2))).|| is V11() real ext-real Element of REAL
(x1 /. x1) - ((p /. x2) + (x1 /. x2)) is Element of the carrier of X
(p /. x1) + ((x1 /. x1) - ((p /. x2) + (x1 /. x2))) is Element of the carrier of X
||.((p /. x1) + ((x1 /. x1) - ((p /. x2) + (x1 /. x2)))).|| is V11() real ext-real Element of REAL
(x1 /. x1) - (p /. x2) is Element of the carrier of X
((x1 /. x1) - (p /. x2)) - (x1 /. x2) is Element of the carrier of X
(p /. x1) + (((x1 /. x1) - (p /. x2)) - (x1 /. x2)) is Element of the carrier of X
||.((p /. x1) + (((x1 /. x1) - (p /. x2)) - (x1 /. x2))).|| is V11() real ext-real Element of REAL
- (p /. x2) is Element of the carrier of X
(- (p /. x2)) + (x1 /. x1) is Element of the carrier of X
((- (p /. x2)) + (x1 /. x1)) - (x1 /. x2) is Element of the carrier of X
(p /. x1) + (((- (p /. x2)) + (x1 /. x1)) - (x1 /. x2)) is Element of the carrier of X
||.((p /. x1) + (((- (p /. x2)) + (x1 /. x1)) - (x1 /. x2))).|| is V11() real ext-real Element of REAL
(- (p /. x2)) + ((x1 /. x1) - (x1 /. x2)) is Element of the carrier of X
(p /. x1) + ((- (p /. x2)) + ((x1 /. x1) - (x1 /. x2))) is Element of the carrier of X
||.((p /. x1) + ((- (p /. x2)) + ((x1 /. x1) - (x1 /. x2)))).|| is V11() real ext-real Element of REAL
(p /. x1) + (- (p /. x2)) is Element of the carrier of X
((p /. x1) + (- (p /. x2))) + ((x1 /. x1) - (x1 /. x2)) is Element of the carrier of X
||.(((p /. x1) + (- (p /. x2))) + ((x1 /. x1) - (x1 /. x2))).|| is V11() real ext-real Element of REAL
((p /. x1) - (p /. x2)) + ((x1 /. x1) - (x1 /. x2)) is Element of the carrier of X
||.(((p /. x1) - (p /. x2)) + ((x1 /. x1) - (x1 /. x2))).|| is V11() real ext-real Element of REAL
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of X is non empty set
K7( the carrier of X, the carrier of CNS) is set
K6(K7( the carrier of X, the carrier of CNS)) is set
f is set
x0 is set
f /\ x0 is set
p is Relation-like the carrier of X -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of X, the carrier of CNS))
x1 is Relation-like the carrier of X -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of X, the carrier of CNS))
p + x1 is Relation-like the carrier of X -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of X, the carrier of CNS))
x2 is V11() real ext-real Element of REAL
dom x1 is Element of K6( the carrier of X)
K6( the carrier of X) is set
dom p is Element of K6( the carrier of X)
(dom p) /\ (dom x1) is Element of K6( the carrier of X)
dom (p + x1) is Element of K6( the carrier of X)
s9 is V11() real ext-real Element of REAL
x2 + s9 is V11() real ext-real Element of REAL
x1 is V11() real ext-real Element of REAL
0 + 0 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative Element of REAL
x1 is Element of the carrier of X
x2 is Element of the carrier of X
(p + x1) /. x1 is Element of the carrier of CNS
(p + x1) /. x2 is Element of the carrier of CNS
((p + x1) /. x1) - ((p + x1) /. x2) is Element of the carrier of CNS
||.(((p + x1) /. x1) - ((p + x1) /. x2)).|| is V11() real ext-real Element of REAL
x1 - x2 is Element of the carrier of X
||.(x1 - x2).|| is V11() real ext-real Element of REAL
x1 * ||.(x1 - x2).|| is V11() real ext-real Element of REAL
x1 /. x1 is Element of the carrier of CNS
x1 /. x2 is Element of the carrier of CNS
(x1 /. x1) - (x1 /. x2) is Element of the carrier of CNS
||.((x1 /. x1) - (x1 /. x2)).|| is V11() real ext-real Element of REAL
s9 * ||.(x1 - x2).|| is V11() real ext-real Element of REAL
p /. x1 is Element of the carrier of CNS
p /. x2 is Element of the carrier of CNS
(p /. x1) - (p /. x2) is Element of the carrier of CNS
||.((p /. x1) - (p /. x2)).|| is V11() real ext-real Element of REAL
x2 * ||.(x1 - x2).|| is V11() real ext-real Element of REAL
||.((p /. x1) - (p /. x2)).|| + ||.((x1 /. x1) - (x1 /. x2)).|| is V11() real ext-real Element of REAL
(x2 * ||.(x1 - x2).||) + (s9 * ||.(x1 - x2).||) is V11() real ext-real Element of REAL
(p /. x1) + (x1 /. x1) is Element of the carrier of CNS
((p /. x1) + (x1 /. x1)) - ((p + x1) /. x2) is Element of the carrier of CNS
||.(((p /. x1) + (x1 /. x1)) - ((p + x1) /. x2)).|| is V11() real ext-real Element of REAL
(p /. x2) + (x1 /. x2) is Element of the carrier of CNS
((p /. x1) + (x1 /. x1)) - ((p /. x2) + (x1 /. x2)) is Element of the carrier of CNS
||.(((p /. x1) + (x1 /. x1)) - ((p /. x2) + (x1 /. x2))).|| is V11() real ext-real Element of REAL
(x1 /. x1) - ((p /. x2) + (x1 /. x2)) is Element of the carrier of CNS
(p /. x1) + ((x1 /. x1) - ((p /. x2) + (x1 /. x2))) is Element of the carrier of CNS
||.((p /. x1) + ((x1 /. x1) - ((p /. x2) + (x1 /. x2)))).|| is V11() real ext-real Element of REAL
(x1 /. x1) - (p /. x2) is Element of the carrier of CNS
((x1 /. x1) - (p /. x2)) - (x1 /. x2) is Element of the carrier of CNS
(p /. x1) + (((x1 /. x1) - (p /. x2)) - (x1 /. x2)) is Element of the carrier of CNS
||.((p /. x1) + (((x1 /. x1) - (p /. x2)) - (x1 /. x2))).|| is V11() real ext-real Element of REAL
- (p /. x2) is Element of the carrier of CNS
(- (p /. x2)) + (x1 /. x1) is Element of the carrier of CNS
((- (p /. x2)) + (x1 /. x1)) - (x1 /. x2) is Element of the carrier of CNS
(p /. x1) + (((- (p /. x2)) + (x1 /. x1)) - (x1 /. x2)) is Element of the carrier of CNS
||.((p /. x1) + (((- (p /. x2)) + (x1 /. x1)) - (x1 /. x2))).|| is V11() real ext-real Element of REAL
(- (p /. x2)) + ((x1 /. x1) - (x1 /. x2)) is Element of the carrier of CNS
(p /. x1) + ((- (p /. x2)) + ((x1 /. x1) - (x1 /. x2))) is Element of the carrier of CNS
||.((p /. x1) + ((- (p /. x2)) + ((x1 /. x1) - (x1 /. x2)))).|| is V11() real ext-real Element of REAL
(p /. x1) + (- (p /. x2)) is Element of the carrier of CNS
((p /. x1) + (- (p /. x2))) + ((x1 /. x1) - (x1 /. x2)) is Element of the carrier of CNS
||.(((p /. x1) + (- (p /. x2))) + ((x1 /. x1) - (x1 /. x2))).|| is V11() real ext-real Element of REAL
((p /. x1) - (p /. x2)) + ((x1 /. x1) - (x1 /. x2)) is Element of the carrier of CNS
||.(((p /. x1) - (p /. x2)) + ((x1 /. x1) - (x1 /. x2))).|| is V11() real ext-real Element of REAL
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of X is non empty set
K7( the carrier of CNS, the carrier of X) is set
K6(K7( the carrier of CNS, the carrier of X)) is set
f is set
x0 is set
f /\ x0 is set
p is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
x1 is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
p - x1 is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
x2 is V11() real ext-real Element of REAL
dom x1 is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
dom p is Element of K6( the carrier of CNS)
(dom p) /\ (dom x1) is Element of K6( the carrier of CNS)
dom (p - x1) is Element of K6( the carrier of CNS)
s9 is V11() real ext-real Element of REAL
x2 + s9 is V11() real ext-real Element of REAL
x1 is V11() real ext-real Element of REAL
0 + 0 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative Element of REAL
x1 is Element of the carrier of CNS
x2 is Element of the carrier of CNS
(p - x1) /. x1 is Element of the carrier of X
(p - x1) /. x2 is Element of the carrier of X
((p - x1) /. x1) - ((p - x1) /. x2) is Element of the carrier of X
||.(((p - x1) /. x1) - ((p - x1) /. x2)).|| is V11() real ext-real Element of REAL
x1 - x2 is Element of the carrier of CNS
||.(x1 - x2).|| is V11() real ext-real Element of REAL
x1 * ||.(x1 - x2).|| is V11() real ext-real Element of REAL
x1 /. x1 is Element of the carrier of X
x1 /. x2 is Element of the carrier of X
(x1 /. x1) - (x1 /. x2) is Element of the carrier of X
||.((x1 /. x1) - (x1 /. x2)).|| is V11() real ext-real Element of REAL
s9 * ||.(x1 - x2).|| is V11() real ext-real Element of REAL
p /. x1 is Element of the carrier of X
p /. x2 is Element of the carrier of X
(p /. x1) - (p /. x2) is Element of the carrier of X
||.((p /. x1) - (p /. x2)).|| is V11() real ext-real Element of REAL
x2 * ||.(x1 - x2).|| is V11() real ext-real Element of REAL
||.((p /. x1) - (p /. x2)).|| + ||.((x1 /. x1) - (x1 /. x2)).|| is V11() real ext-real Element of REAL
(x2 * ||.(x1 - x2).||) + (s9 * ||.(x1 - x2).||) is V11() real ext-real Element of REAL
(p /. x1) - (x1 /. x1) is Element of the carrier of X
((p /. x1) - (x1 /. x1)) - ((p - x1) /. x2) is Element of the carrier of X
||.(((p /. x1) - (x1 /. x1)) - ((p - x1) /. x2)).|| is V11() real ext-real Element of REAL
(p /. x2) - (x1 /. x2) is Element of the carrier of X
((p /. x1) - (x1 /. x1)) - ((p /. x2) - (x1 /. x2)) is Element of the carrier of X
||.(((p /. x1) - (x1 /. x1)) - ((p /. x2) - (x1 /. x2))).|| is V11() real ext-real Element of REAL
(x1 /. x1) + ((p /. x2) - (x1 /. x2)) is Element of the carrier of X
(p /. x1) - ((x1 /. x1) + ((p /. x2) - (x1 /. x2))) is Element of the carrier of X
||.((p /. x1) - ((x1 /. x1) + ((p /. x2) - (x1 /. x2)))).|| is V11() real ext-real Element of REAL
(p /. x2) + (x1 /. x1) is Element of the carrier of X
((p /. x2) + (x1 /. x1)) - (x1 /. x2) is Element of the carrier of X
(p /. x1) - (((p /. x2) + (x1 /. x1)) - (x1 /. x2)) is Element of the carrier of X
||.((p /. x1) - (((p /. x2) + (x1 /. x1)) - (x1 /. x2))).|| is V11() real ext-real Element of REAL
(p /. x2) + ((x1 /. x1) - (x1 /. x2)) is Element of the carrier of X
(p /. x1) - ((p /. x2) + ((x1 /. x1) - (x1 /. x2))) is Element of the carrier of X
||.((p /. x1) - ((p /. x2) + ((x1 /. x1) - (x1 /. x2)))).|| is V11() real ext-real Element of REAL
((p /. x1) - (p /. x2)) - ((x1 /. x1) - (x1 /. x2)) is Element of the carrier of X
||.(((p /. x1) - (p /. x2)) - ((x1 /. x1) - (x1 /. x2))).|| is V11() real ext-real Element of REAL
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of X is non empty set
K7( the carrier of CNS, the carrier of X) is set
K6(K7( the carrier of CNS, the carrier of X)) is set
f is set
x0 is set
f /\ x0 is set
p is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
x1 is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
p - x1 is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
x2 is V11() real ext-real Element of REAL
dom x1 is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
dom p is Element of K6( the carrier of CNS)
(dom p) /\ (dom x1) is Element of K6( the carrier of CNS)
dom (p - x1) is Element of K6( the carrier of CNS)
s9 is V11() real ext-real Element of REAL
x2 + s9 is V11() real ext-real Element of REAL
x1 is V11() real ext-real Element of REAL
0 + 0 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative Element of REAL
x1 is Element of the carrier of CNS
x2 is Element of the carrier of CNS
(p - x1) /. x1 is Element of the carrier of X
(p - x1) /. x2 is Element of the carrier of X
((p - x1) /. x1) - ((p - x1) /. x2) is Element of the carrier of X
||.(((p - x1) /. x1) - ((p - x1) /. x2)).|| is V11() real ext-real Element of REAL
x1 - x2 is Element of the carrier of CNS
||.(x1 - x2).|| is V11() real ext-real Element of REAL
x1 * ||.(x1 - x2).|| is V11() real ext-real Element of REAL
x1 /. x1 is Element of the carrier of X
x1 /. x2 is Element of the carrier of X
(x1 /. x1) - (x1 /. x2) is Element of the carrier of X
||.((x1 /. x1) - (x1 /. x2)).|| is V11() real ext-real Element of REAL
s9 * ||.(x1 - x2).|| is V11() real ext-real Element of REAL
p /. x1 is Element of the carrier of X
p /. x2 is Element of the carrier of X
(p /. x1) - (p /. x2) is Element of the carrier of X
||.((p /. x1) - (p /. x2)).|| is V11() real ext-real Element of REAL
x2 * ||.(x1 - x2).|| is V11() real ext-real Element of REAL
||.((p /. x1) - (p /. x2)).|| + ||.((x1 /. x1) - (x1 /. x2)).|| is V11() real ext-real Element of REAL
(x2 * ||.(x1 - x2).||) + (s9 * ||.(x1 - x2).||) is V11() real ext-real Element of REAL
(p /. x1) - (x1 /. x1) is Element of the carrier of X
((p /. x1) - (x1 /. x1)) - ((p - x1) /. x2) is Element of the carrier of X
||.(((p /. x1) - (x1 /. x1)) - ((p - x1) /. x2)).|| is V11() real ext-real Element of REAL
(p /. x2) - (x1 /. x2) is Element of the carrier of X
((p /. x1) - (x1 /. x1)) - ((p /. x2) - (x1 /. x2)) is Element of the carrier of X
||.(((p /. x1) - (x1 /. x1)) - ((p /. x2) - (x1 /. x2))).|| is V11() real ext-real Element of REAL
(x1 /. x1) + ((p /. x2) - (x1 /. x2)) is Element of the carrier of X
(p /. x1) - ((x1 /. x1) + ((p /. x2) - (x1 /. x2))) is Element of the carrier of X
||.((p /. x1) - ((x1 /. x1) + ((p /. x2) - (x1 /. x2)))).|| is V11() real ext-real Element of REAL
(p /. x2) + (x1 /. x1) is Element of the carrier of X
((p /. x2) + (x1 /. x1)) - (x1 /. x2) is Element of the carrier of X
(p /. x1) - (((p /. x2) + (x1 /. x1)) - (x1 /. x2)) is Element of the carrier of X
||.((p /. x1) - (((p /. x2) + (x1 /. x1)) - (x1 /. x2))).|| is V11() real ext-real Element of REAL
(p /. x2) + ((x1 /. x1) - (x1 /. x2)) is Element of the carrier of X
(p /. x1) - ((p /. x2) + ((x1 /. x1) - (x1 /. x2))) is Element of the carrier of X
||.((p /. x1) - ((p /. x2) + ((x1 /. x1) - (x1 /. x2)))).|| is V11() real ext-real Element of REAL
((p /. x1) - (p /. x2)) - ((x1 /. x1) - (x1 /. x2)) is Element of the carrier of X
||.(((p /. x1) - (p /. x2)) - ((x1 /. x1) - (x1 /. x2))).|| is V11() real ext-real Element of REAL
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of X is non empty set
K7( the carrier of X, the carrier of CNS) is set
K6(K7( the carrier of X, the carrier of CNS)) is set
f is set
x0 is set
f /\ x0 is set
p is Relation-like the carrier of X -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of X, the carrier of CNS))
x1 is Relation-like the carrier of X -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of X, the carrier of CNS))
p - x1 is Relation-like the carrier of X -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of X, the carrier of CNS))
x2 is V11() real ext-real Element of REAL
dom x1 is Element of K6( the carrier of X)
K6( the carrier of X) is set
dom p is Element of K6( the carrier of X)
(dom p) /\ (dom x1) is Element of K6( the carrier of X)
dom (p - x1) is Element of K6( the carrier of X)
s9 is V11() real ext-real Element of REAL
x2 + s9 is V11() real ext-real Element of REAL
x1 is V11() real ext-real Element of REAL
0 + 0 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative Element of REAL
x1 is Element of the carrier of X
x2 is Element of the carrier of X
(p - x1) /. x1 is Element of the carrier of CNS
(p - x1) /. x2 is Element of the carrier of CNS
((p - x1) /. x1) - ((p - x1) /. x2) is Element of the carrier of CNS
||.(((p - x1) /. x1) - ((p - x1) /. x2)).|| is V11() real ext-real Element of REAL
x1 - x2 is Element of the carrier of X
||.(x1 - x2).|| is V11() real ext-real Element of REAL
x1 * ||.(x1 - x2).|| is V11() real ext-real Element of REAL
x1 /. x1 is Element of the carrier of CNS
x1 /. x2 is Element of the carrier of CNS
(x1 /. x1) - (x1 /. x2) is Element of the carrier of CNS
||.((x1 /. x1) - (x1 /. x2)).|| is V11() real ext-real Element of REAL
s9 * ||.(x1 - x2).|| is V11() real ext-real Element of REAL
p /. x1 is Element of the carrier of CNS
p /. x2 is Element of the carrier of CNS
(p /. x1) - (p /. x2) is Element of the carrier of CNS
||.((p /. x1) - (p /. x2)).|| is V11() real ext-real Element of REAL
x2 * ||.(x1 - x2).|| is V11() real ext-real Element of REAL
||.((p /. x1) - (p /. x2)).|| + ||.((x1 /. x1) - (x1 /. x2)).|| is V11() real ext-real Element of REAL
(x2 * ||.(x1 - x2).||) + (s9 * ||.(x1 - x2).||) is V11() real ext-real Element of REAL
(p /. x1) - (x1 /. x1) is Element of the carrier of CNS
((p /. x1) - (x1 /. x1)) - ((p - x1) /. x2) is Element of the carrier of CNS
||.(((p /. x1) - (x1 /. x1)) - ((p - x1) /. x2)).|| is V11() real ext-real Element of REAL
(p /. x2) - (x1 /. x2) is Element of the carrier of CNS
((p /. x1) - (x1 /. x1)) - ((p /. x2) - (x1 /. x2)) is Element of the carrier of CNS
||.(((p /. x1) - (x1 /. x1)) - ((p /. x2) - (x1 /. x2))).|| is V11() real ext-real Element of REAL
(x1 /. x1) + ((p /. x2) - (x1 /. x2)) is Element of the carrier of CNS
(p /. x1) - ((x1 /. x1) + ((p /. x2) - (x1 /. x2))) is Element of the carrier of CNS
||.((p /. x1) - ((x1 /. x1) + ((p /. x2) - (x1 /. x2)))).|| is V11() real ext-real Element of REAL
(p /. x2) + (x1 /. x1) is Element of the carrier of CNS
((p /. x2) + (x1 /. x1)) - (x1 /. x2) is Element of the carrier of CNS
(p /. x1) - (((p /. x2) + (x1 /. x1)) - (x1 /. x2)) is Element of the carrier of CNS
||.((p /. x1) - (((p /. x2) + (x1 /. x1)) - (x1 /. x2))).|| is V11() real ext-real Element of REAL
(p /. x2) + ((x1 /. x1) - (x1 /. x2)) is Element of the carrier of CNS
(p /. x1) - ((p /. x2) + ((x1 /. x1) - (x1 /. x2))) is Element of the carrier of CNS
||.((p /. x1) - ((p /. x2) + ((x1 /. x1) - (x1 /. x2)))).|| is V11() real ext-real Element of REAL
((p /. x1) - (p /. x2)) - ((x1 /. x1) - (x1 /. x2)) is Element of the carrier of CNS
||.(((p /. x1) - (p /. x2)) - ((x1 /. x1) - (x1 /. x2))).|| is V11() real ext-real Element of REAL
CNS is V11() set
X is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of X is non empty set
f is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of f is non empty set
K7( the carrier of X, the carrier of f) is set
K6(K7( the carrier of X, the carrier of f)) is set
x0 is set
p is Relation-like the carrier of X -defined the carrier of f -valued Function-like Element of K6(K7( the carrier of X, the carrier of f))
CNS (#) p is Relation-like the carrier of X -defined the carrier of f -valued Function-like Element of K6(K7( the carrier of X, the carrier of f))
x1 is V11() real ext-real Element of REAL
dom p is Element of K6( the carrier of X)
K6( the carrier of X) is set
dom (CNS (#) p) is Element of K6( the carrier of X)
x2 is V11() real ext-real Element of REAL
s9 is Element of the carrier of X
x1 is Element of the carrier of X
s9 - x1 is Element of the carrier of X
||.(s9 - x1).|| is V11() real ext-real Element of REAL
x2 * 0 is V11() real ext-real Element of REAL
x2 * ||.(s9 - x1).|| is V11() real ext-real Element of REAL
(CNS (#) p) /. s9 is Element of the carrier of f
(CNS (#) p) /. x1 is Element of the carrier of f
((CNS (#) p) /. s9) - ((CNS (#) p) /. x1) is Element of the carrier of f
||.(((CNS (#) p) /. s9) - ((CNS (#) p) /. x1)).|| is V11() real ext-real Element of REAL
p /. s9 is Element of the carrier of f
CNS * (p /. s9) is Element of the carrier of f
(CNS * (p /. s9)) - ((CNS (#) p) /. x1) is Element of the carrier of f
||.((CNS * (p /. s9)) - ((CNS (#) p) /. x1)).|| is V11() real ext-real Element of REAL
0. f is V97(f) Element of the carrier of f
(0. f) - ((CNS (#) p) /. x1) is Element of the carrier of f
||.((0. f) - ((CNS (#) p) /. x1)).|| is V11() real ext-real Element of REAL
p /. x1 is Element of the carrier of f
CNS * (p /. x1) is Element of the carrier of f
(0. f) - (CNS * (p /. x1)) is Element of the carrier of f
||.((0. f) - (CNS * (p /. x1))).|| is V11() real ext-real Element of REAL
(0. f) - (0. f) is Element of the carrier of f
||.((0. f) - (0. f)).|| is V11() real ext-real Element of REAL
||.(0. f).|| is V11() real ext-real Element of REAL
|.CNS.| is V11() real ext-real Element of REAL
|.CNS.| * x1 is V11() real ext-real Element of REAL
0 * x1 is V11() real ext-real Element of REAL
x2 is V11() real ext-real Element of REAL
s9 is Element of the carrier of X
x1 is Element of the carrier of X
p /. s9 is Element of the carrier of f
p /. x1 is Element of the carrier of f
(p /. s9) - (p /. x1) is Element of the carrier of f
||.((p /. s9) - (p /. x1)).|| is V11() real ext-real Element of REAL
|.CNS.| * ||.((p /. s9) - (p /. x1)).|| is V11() real ext-real Element of REAL
s9 - x1 is Element of the carrier of X
||.(s9 - x1).|| is V11() real ext-real Element of REAL
x1 * ||.(s9 - x1).|| is V11() real ext-real Element of REAL
|.CNS.| * (x1 * ||.(s9 - x1).||) is V11() real ext-real Element of REAL
(CNS (#) p) /. s9 is Element of the carrier of f
(CNS (#) p) /. x1 is Element of the carrier of f
((CNS (#) p) /. s9) - ((CNS (#) p) /. x1) is Element of the carrier of f
||.(((CNS (#) p) /. s9) - ((CNS (#) p) /. x1)).|| is V11() real ext-real Element of REAL
CNS * (p /. s9) is Element of the carrier of f
(CNS * (p /. s9)) - ((CNS (#) p) /. x1) is Element of the carrier of f
||.((CNS * (p /. s9)) - ((CNS (#) p) /. x1)).|| is V11() real ext-real Element of REAL
CNS * (p /. x1) is Element of the carrier of f
(CNS * (p /. s9)) - (CNS * (p /. x1)) is Element of the carrier of f
||.((CNS * (p /. s9)) - (CNS * (p /. x1))).|| is V11() real ext-real Element of REAL
CNS * ((p /. s9) - (p /. x1)) is Element of the carrier of f
||.(CNS * ((p /. s9) - (p /. x1))).|| is V11() real ext-real Element of REAL
x2 * ||.(s9 - x1).|| is V11() real ext-real Element of REAL
x2 is V11() real ext-real Element of REAL
CNS is V11() real ext-real Element of REAL
X is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of X is non empty set
f is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of f is non empty set
K7( the carrier of X, the carrier of f) is set
K6(K7( the carrier of X, the carrier of f)) is set
x0 is set
p is Relation-like the carrier of X -defined the carrier of f -valued Function-like Element of K6(K7( the carrier of X, the carrier of f))
CNS (#) p is Relation-like the carrier of X -defined the carrier of f -valued Function-like Element of K6(K7( the carrier of X, the carrier of f))
x1 is V11() real ext-real Element of REAL
dom p is Element of K6( the carrier of X)
K6( the carrier of X) is set
dom (CNS (#) p) is Element of K6( the carrier of X)
x2 is V11() real ext-real Element of REAL
s9 is Element of the carrier of X
x1 is Element of the carrier of X
s9 - x1 is Element of the carrier of X
||.(s9 - x1).|| is V11() real ext-real Element of REAL
x2 * 0 is V11() real ext-real Element of REAL
x2 * ||.(s9 - x1).|| is V11() real ext-real Element of REAL
(CNS (#) p) /. s9 is Element of the carrier of f
(CNS (#) p) /. x1 is Element of the carrier of f
((CNS (#) p) /. s9) - ((CNS (#) p) /. x1) is Element of the carrier of f
||.(((CNS (#) p) /. s9) - ((CNS (#) p) /. x1)).|| is V11() real ext-real Element of REAL
p /. s9 is Element of the carrier of f
CNS * (p /. s9) is Element of the carrier of f
(CNS * (p /. s9)) - ((CNS (#) p) /. x1) is Element of the carrier of f
||.((CNS * (p /. s9)) - ((CNS (#) p) /. x1)).|| is V11() real ext-real Element of REAL
0. f is V97(f) Element of the carrier of f
(0. f) - ((CNS (#) p) /. x1) is Element of the carrier of f
||.((0. f) - ((CNS (#) p) /. x1)).|| is V11() real ext-real Element of REAL
p /. x1 is Element of the carrier of f
CNS * (p /. x1) is Element of the carrier of f
(0. f) - (CNS * (p /. x1)) is Element of the carrier of f
||.((0. f) - (CNS * (p /. x1))).|| is V11() real ext-real Element of REAL
(0. f) - (0. f) is Element of the carrier of f
||.((0. f) - (0. f)).|| is V11() real ext-real Element of REAL
||.(0. f).|| is V11() real ext-real Element of REAL
abs CNS is V11() real ext-real Element of REAL
(abs CNS) * x1 is V11() real ext-real Element of REAL
0 * x1 is V11() real ext-real Element of REAL
x2 is V11() real ext-real Element of REAL
s9 is Element of the carrier of X
x1 is Element of the carrier of X
p /. s9 is Element of the carrier of f
p /. x1 is Element of the carrier of f
(p /. s9) - (p /. x1) is Element of the carrier of f
||.((p /. s9) - (p /. x1)).|| is V11() real ext-real Element of REAL
(abs CNS) * ||.((p /. s9) - (p /. x1)).|| is V11() real ext-real Element of REAL
s9 - x1 is Element of the carrier of X
||.(s9 - x1).|| is V11() real ext-real Element of REAL
x1 * ||.(s9 - x1).|| is V11() real ext-real Element of REAL
(abs CNS) * (x1 * ||.(s9 - x1).||) is V11() real ext-real Element of REAL
(CNS (#) p) /. s9 is Element of the carrier of f
(CNS (#) p) /. x1 is Element of the carrier of f
((CNS (#) p) /. s9) - ((CNS (#) p) /. x1) is Element of the carrier of f
||.(((CNS (#) p) /. s9) - ((CNS (#) p) /. x1)).|| is V11() real ext-real Element of REAL
CNS * (p /. s9) is Element of the carrier of f
(CNS * (p /. s9)) - ((CNS (#) p) /. x1) is Element of the carrier of f
||.((CNS * (p /. s9)) - ((CNS (#) p) /. x1)).|| is V11() real ext-real Element of REAL
CNS * (p /. x1) is Element of the carrier of f
(CNS * (p /. s9)) - (CNS * (p /. x1)) is Element of the carrier of f
||.((CNS * (p /. s9)) - (CNS * (p /. x1))).|| is V11() real ext-real Element of REAL
CNS * ((p /. s9) - (p /. x1)) is Element of the carrier of f
||.(CNS * ((p /. s9) - (p /. x1))).|| is V11() real ext-real Element of REAL
x2 * ||.(s9 - x1).|| is V11() real ext-real Element of REAL
x2 is V11() real ext-real Element of REAL
CNS is V11() set
X is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of X is non empty set
f is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of f is non empty set
K7( the carrier of f, the carrier of X) is set
K6(K7( the carrier of f, the carrier of X)) is set
x0 is set
p is Relation-like the carrier of f -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of f, the carrier of X))
CNS (#) p is Relation-like the carrier of f -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of f, the carrier of X))
x1 is V11() real ext-real Element of REAL
dom p is Element of K6( the carrier of f)
K6( the carrier of f) is set
dom (CNS (#) p) is Element of K6( the carrier of f)
x2 is V11() real ext-real Element of REAL
s9 is Element of the carrier of f
x1 is Element of the carrier of f
s9 - x1 is Element of the carrier of f
||.(s9 - x1).|| is V11() real ext-real Element of REAL
x2 * 0 is V11() real ext-real Element of REAL
x2 * ||.(s9 - x1).|| is V11() real ext-real Element of REAL
(CNS (#) p) /. s9 is Element of the carrier of X
(CNS (#) p) /. x1 is Element of the carrier of X
((CNS (#) p) /. s9) - ((CNS (#) p) /. x1) is Element of the carrier of X
||.(((CNS (#) p) /. s9) - ((CNS (#) p) /. x1)).|| is V11() real ext-real Element of REAL
p /. s9 is Element of the carrier of X
CNS * (p /. s9) is Element of the carrier of X
(CNS * (p /. s9)) - ((CNS (#) p) /. x1) is Element of the carrier of X
||.((CNS * (p /. s9)) - ((CNS (#) p) /. x1)).|| is V11() real ext-real Element of REAL
0. X is V97(X) Element of the carrier of X
(0. X) - ((CNS (#) p) /. x1) is Element of the carrier of X
||.((0. X) - ((CNS (#) p) /. x1)).|| is V11() real ext-real Element of REAL
p /. x1 is Element of the carrier of X
CNS * (p /. x1) is Element of the carrier of X
(0. X) - (CNS * (p /. x1)) is Element of the carrier of X
||.((0. X) - (CNS * (p /. x1))).|| is V11() real ext-real Element of REAL
(0. X) - (0. X) is Element of the carrier of X
||.((0. X) - (0. X)).|| is V11() real ext-real Element of REAL
||.(0. X).|| is V11() real ext-real Element of REAL
|.CNS.| is V11() real ext-real Element of REAL
|.CNS.| * x1 is V11() real ext-real Element of REAL
0 * x1 is V11() real ext-real Element of REAL
x2 is V11() real ext-real Element of REAL
s9 is Element of the carrier of f
x1 is Element of the carrier of f
p /. s9 is Element of the carrier of X
p /. x1 is Element of the carrier of X
(p /. s9) - (p /. x1) is Element of the carrier of X
||.((p /. s9) - (p /. x1)).|| is V11() real ext-real Element of REAL
|.CNS.| * ||.((p /. s9) - (p /. x1)).|| is V11() real ext-real Element of REAL
s9 - x1 is Element of the carrier of f
||.(s9 - x1).|| is V11() real ext-real Element of REAL
x1 * ||.(s9 - x1).|| is V11() real ext-real Element of REAL
|.CNS.| * (x1 * ||.(s9 - x1).||) is V11() real ext-real Element of REAL
(CNS (#) p) /. s9 is Element of the carrier of X
(CNS (#) p) /. x1 is Element of the carrier of X
((CNS (#) p) /. s9) - ((CNS (#) p) /. x1) is Element of the carrier of X
||.(((CNS (#) p) /. s9) - ((CNS (#) p) /. x1)).|| is V11() real ext-real Element of REAL
CNS * (p /. s9) is Element of the carrier of X
(CNS * (p /. s9)) - ((CNS (#) p) /. x1) is Element of the carrier of X
||.((CNS * (p /. s9)) - ((CNS (#) p) /. x1)).|| is V11() real ext-real Element of REAL
CNS * (p /. x1) is Element of the carrier of X
(CNS * (p /. s9)) - (CNS * (p /. x1)) is Element of the carrier of X
||.((CNS * (p /. s9)) - (CNS * (p /. x1))).|| is V11() real ext-real Element of REAL
CNS * ((p /. s9) - (p /. x1)) is Element of the carrier of X
||.(CNS * ((p /. s9) - (p /. x1))).|| is V11() real ext-real Element of REAL
x2 * ||.(s9 - x1).|| is V11() real ext-real Element of REAL
x2 is V11() real ext-real Element of REAL
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of X is non empty set
K7( the carrier of CNS, the carrier of X) is set
K6(K7( the carrier of CNS, the carrier of X)) is set
f is set
x0 is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
- x0 is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
||.x0.|| is Relation-like the carrier of CNS -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7( the carrier of CNS,REAL))
K7( the carrier of CNS,REAL) is complex-valued ext-real-valued real-valued set
K6(K7( the carrier of CNS,REAL)) is set
p is V11() real ext-real Element of REAL
(- 1r) (#) x0 is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
dom x0 is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
dom ||.x0.|| is Element of K6( the carrier of CNS)
x1 is Element of the carrier of CNS
x2 is Element of the carrier of CNS
||.x0.|| /. x1 is V11() real ext-real Element of REAL
||.x0.|| /. x2 is V11() real ext-real Element of REAL
(||.x0.|| /. x1) - (||.x0.|| /. x2) is V11() real ext-real Element of REAL
abs ((||.x0.|| /. x1) - (||.x0.|| /. x2)) is V11() real ext-real Element of REAL
x1 - x2 is Element of the carrier of CNS
||.(x1 - x2).|| is V11() real ext-real Element of REAL
p * ||.(x1 - x2).|| is V11() real ext-real Element of REAL
||.x0.|| . x1 is V11() real ext-real Element of REAL
(||.x0.|| . x1) - (||.x0.|| /. x2) is V11() real ext-real Element of REAL
abs ((||.x0.|| . x1) - (||.x0.|| /. x2)) is V11() real ext-real Element of REAL
||.x0.|| . x2 is V11() real ext-real Element of REAL
(||.x0.|| . x1) - (||.x0.|| . x2) is V11() real ext-real Element of REAL
abs ((||.x0.|| . x1) - (||.x0.|| . x2)) is V11() real ext-real Element of REAL
x0 /. x1 is Element of the carrier of X
||.(x0 /. x1).|| is V11() real ext-real Element of REAL
||.(x0 /. x1).|| - (||.x0.|| . x2) is V11() real ext-real Element of REAL
abs (||.(x0 /. x1).|| - (||.x0.|| . x2)) is V11() real ext-real Element of REAL
x0 /. x2 is Element of the carrier of X
||.(x0 /. x2).|| is V11() real ext-real Element of REAL
||.(x0 /. x1).|| - ||.(x0 /. x2).|| is V11() real ext-real Element of REAL
abs (||.(x0 /. x1).|| - ||.(x0 /. x2).||) is V11() real ext-real Element of REAL
(x0 /. x1) - (x0 /. x2) is Element of the carrier of X
||.((x0 /. x1) - (x0 /. x2)).|| is V11() real ext-real Element of REAL
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of X is non empty set
K7( the carrier of CNS, the carrier of X) is set
K6(K7( the carrier of CNS, the carrier of X)) is set
f is set
x0 is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
- x0 is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
||.x0.|| is Relation-like the carrier of CNS -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7( the carrier of CNS,REAL))
K7( the carrier of CNS,REAL) is complex-valued ext-real-valued real-valued set
K6(K7( the carrier of CNS,REAL)) is set
p is V11() real ext-real Element of REAL
(- 1) (#) x0 is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
dom x0 is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
dom ||.x0.|| is Element of K6( the carrier of CNS)
x1 is Element of the carrier of CNS
x2 is Element of the carrier of CNS
||.x0.|| /. x1 is V11() real ext-real Element of REAL
||.x0.|| /. x2 is V11() real ext-real Element of REAL
(||.x0.|| /. x1) - (||.x0.|| /. x2) is V11() real ext-real Element of REAL
abs ((||.x0.|| /. x1) - (||.x0.|| /. x2)) is V11() real ext-real Element of REAL
x1 - x2 is Element of the carrier of CNS
||.(x1 - x2).|| is V11() real ext-real Element of REAL
p * ||.(x1 - x2).|| is V11() real ext-real Element of REAL
||.x0.|| . x1 is V11() real ext-real Element of REAL
(||.x0.|| . x1) - (||.x0.|| /. x2) is V11() real ext-real Element of REAL
abs ((||.x0.|| . x1) - (||.x0.|| /. x2)) is V11() real ext-real Element of REAL
||.x0.|| . x2 is V11() real ext-real Element of REAL
(||.x0.|| . x1) - (||.x0.|| . x2) is V11() real ext-real Element of REAL
abs ((||.x0.|| . x1) - (||.x0.|| . x2)) is V11() real ext-real Element of REAL
x0 /. x1 is Element of the carrier of X
||.(x0 /. x1).|| is V11() real ext-real Element of REAL
||.(x0 /. x1).|| - (||.x0.|| . x2) is V11() real ext-real Element of REAL
abs (||.(x0 /. x1).|| - (||.x0.|| . x2)) is V11() real ext-real Element of REAL
x0 /. x2 is Element of the carrier of X
||.(x0 /. x2).|| is V11() real ext-real Element of REAL
||.(x0 /. x1).|| - ||.(x0 /. x2).|| is V11() real ext-real Element of REAL
abs (||.(x0 /. x1).|| - ||.(x0 /. x2).||) is V11() real ext-real Element of REAL
(x0 /. x1) - (x0 /. x2) is Element of the carrier of X
||.((x0 /. x1) - (x0 /. x2)).|| is V11() real ext-real Element of REAL
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of X is non empty set
K7( the carrier of X, the carrier of CNS) is set
K6(K7( the carrier of X, the carrier of CNS)) is set
f is set
x0 is Relation-like the carrier of X -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of X, the carrier of CNS))
- x0 is Relation-like the carrier of X -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of X, the carrier of CNS))
||.x0.|| is Relation-like the carrier of X -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7( the carrier of X,REAL))
K7( the carrier of X,REAL) is complex-valued ext-real-valued real-valued set
K6(K7( the carrier of X,REAL)) is set
p is V11() real ext-real Element of REAL
(- 1r) (#) x0 is Relation-like the carrier of X -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of X, the carrier of CNS))
dom x0 is Element of K6( the carrier of X)
K6( the carrier of X) is set
dom ||.x0.|| is Element of K6( the carrier of X)
x1 is Element of the carrier of X
x2 is Element of the carrier of X
||.x0.|| /. x1 is V11() real ext-real Element of REAL
||.x0.|| /. x2 is V11() real ext-real Element of REAL
(||.x0.|| /. x1) - (||.x0.|| /. x2) is V11() real ext-real Element of REAL
abs ((||.x0.|| /. x1) - (||.x0.|| /. x2)) is V11() real ext-real Element of REAL
x1 - x2 is Element of the carrier of X
||.(x1 - x2).|| is V11() real ext-real Element of REAL
p * ||.(x1 - x2).|| is V11() real ext-real Element of REAL
||.x0.|| . x1 is V11() real ext-real Element of REAL
(||.x0.|| . x1) - (||.x0.|| /. x2) is V11() real ext-real Element of REAL
abs ((||.x0.|| . x1) - (||.x0.|| /. x2)) is V11() real ext-real Element of REAL
||.x0.|| . x2 is V11() real ext-real Element of REAL
(||.x0.|| . x1) - (||.x0.|| . x2) is V11() real ext-real Element of REAL
abs ((||.x0.|| . x1) - (||.x0.|| . x2)) is V11() real ext-real Element of REAL
x0 /. x1 is Element of the carrier of CNS
||.(x0 /. x1).|| is V11() real ext-real Element of REAL
||.(x0 /. x1).|| - (||.x0.|| . x2) is V11() real ext-real Element of REAL
abs (||.(x0 /. x1).|| - (||.x0.|| . x2)) is V11() real ext-real Element of REAL
x0 /. x2 is Element of the carrier of CNS
||.(x0 /. x2).|| is V11() real ext-real Element of REAL
||.(x0 /. x1).|| - ||.(x0 /. x2).|| is V11() real ext-real Element of REAL
abs (||.(x0 /. x1).|| - ||.(x0 /. x2).||) is V11() real ext-real Element of REAL
(x0 /. x1) - (x0 /. x2) is Element of the carrier of CNS
||.((x0 /. x1) - (x0 /. x2)).|| is V11() real ext-real Element of REAL
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of X is non empty set
K7( the carrier of CNS, the carrier of X) is set
K6(K7( the carrier of CNS, the carrier of X)) is set
f is set
x0 is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
dom x0 is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
x0 | f is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
p is Element of the carrier of CNS
x1 is Element of the carrier of CNS
f /\ (dom x0) is Element of K6( the carrier of CNS)
x0 /. p is Element of the carrier of X
x0 . p is set
x0 . x1 is set
x0 /. x1 is Element of the carrier of X
(x0 /. p) - (x0 /. x1) is Element of the carrier of X
||.((x0 /. p) - (x0 /. x1)).|| is V11() real ext-real Element of REAL
0. X is V97(X) Element of the carrier of X
||.(0. X).|| is V11() real ext-real Element of REAL
p - x1 is Element of the carrier of CNS
||.(p - x1).|| is V11() real ext-real Element of REAL
1 * ||.(p - x1).|| is V11() real ext-real Element of REAL
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of X is non empty set
K7( the carrier of CNS, the carrier of X) is set
K6(K7( the carrier of CNS, the carrier of X)) is set
f is set
x0 is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
dom x0 is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
x0 | f is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
p is Element of the carrier of CNS
x1 is Element of the carrier of CNS
f /\ (dom x0) is Element of K6( the carrier of CNS)
x0 /. p is Element of the carrier of X
x0 . p is set
x0 . x1 is set
x0 /. x1 is Element of the carrier of X
(x0 /. p) - (x0 /. x1) is Element of the carrier of X
||.((x0 /. p) - (x0 /. x1)).|| is V11() real ext-real Element of REAL
0. X is V97(X) Element of the carrier of X
||.(0. X).|| is V11() real ext-real Element of REAL
p - x1 is Element of the carrier of CNS
||.(p - x1).|| is V11() real ext-real Element of REAL
1 * ||.(p - x1).|| is V11() real ext-real Element of REAL
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of X is non empty set
K7( the carrier of X, the carrier of CNS) is set
K6(K7( the carrier of X, the carrier of CNS)) is set
f is set
x0 is Relation-like the carrier of X -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of X, the carrier of CNS))
dom x0 is Element of K6( the carrier of X)
K6( the carrier of X) is set
x0 | f is Relation-like the carrier of X -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of X, the carrier of CNS))
p is Element of the carrier of X
x1 is Element of the carrier of X
f /\ (dom x0) is Element of K6( the carrier of X)
x0 /. p is Element of the carrier of CNS
x0 . p is set
x0 . x1 is set
x0 /. x1 is Element of the carrier of CNS
(x0 /. p) - (x0 /. x1) is Element of the carrier of CNS
||.((x0 /. p) - (x0 /. x1)).|| is V11() real ext-real Element of REAL
0. CNS is V97(CNS) Element of the carrier of CNS
||.(0. CNS).|| is V11() real ext-real Element of REAL
p - x1 is Element of the carrier of X
||.(p - x1).|| is V11() real ext-real Element of REAL
1 * ||.(p - x1).|| is V11() real ext-real Element of REAL
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
K6( the carrier of CNS) is set
f is Element of K6( the carrier of CNS)
id f is Relation-like the carrier of CNS -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of CNS))
K7( the carrier of CNS, the carrier of CNS) is set
K6(K7( the carrier of CNS, the carrier of CNS)) is set
dom (id f) is Element of K6( the carrier of CNS)
X is V11() real ext-real Element of REAL
x0 is Element of the carrier of CNS
p is Element of the carrier of CNS
(id f) /. x0 is Element of the carrier of CNS
(id f) /. p is Element of the carrier of CNS
((id f) /. x0) - ((id f) /. p) is Element of the carrier of CNS
||.(((id f) /. x0) - ((id f) /. p)).|| is V11() real ext-real Element of REAL
x0 - p is Element of the carrier of CNS
||.(x0 - p).|| is V11() real ext-real Element of REAL
X * ||.(x0 - p).|| is V11() real ext-real Element of REAL
x0 - ((id f) /. p) is Element of the carrier of CNS
||.(x0 - ((id f) /. p)).|| is V11() real ext-real Element of REAL
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of X is non empty set
K7( the carrier of CNS, the carrier of X) is set
K6(K7( the carrier of CNS, the carrier of X)) is set
f is set
x0 is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
p is V11() real ext-real Element of REAL
dom x0 is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
x0 | f is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
dom (x0 | f) is Element of K6( the carrier of CNS)
x1 is Element of the carrier of CNS
x2 is V11() real ext-real Element of REAL
x2 / p is V11() real ext-real Element of REAL
x1 is Element of the carrier of CNS
x1 - x1 is Element of the carrier of CNS
||.(x1 - x1).|| is V11() real ext-real Element of REAL
(x2 / p) * p is V11() real ext-real Element of REAL
p * ||.(x1 - x1).|| is V11() real ext-real Element of REAL
x0 /. x1 is Element of the carrier of X
x0 /. x1 is Element of the carrier of X
(x0 /. x1) - (x0 /. x1) is Element of the carrier of X
||.((x0 /. x1) - (x0 /. x1)).|| is V11() real ext-real Element of REAL
(x0 | f) /. x1 is Element of the carrier of X
((x0 | f) /. x1) - (x0 /. x1) is Element of the carrier of X
||.(((x0 | f) /. x1) - (x0 /. x1)).|| is V11() real ext-real Element of REAL
(x0 | f) /. x1 is Element of the carrier of X
((x0 | f) /. x1) - ((x0 | f) /. x1) is Element of the carrier of X
||.(((x0 | f) /. x1) - ((x0 | f) /. x1)).|| is V11() real ext-real Element of REAL
p " is V11() real ext-real Element of REAL
x1 is V11() real ext-real Element of REAL
x2 * (p ") is V11() real ext-real Element of REAL
x1 is Element of the carrier of CNS
x1 - x1 is Element of the carrier of CNS
||.(x1 - x1).|| is V11() real ext-real Element of REAL
(x0 | f) /. x1 is Element of the carrier of X
((x0 | f) /. x1) - ((x0 | f) /. x1) is Element of the carrier of X
||.(((x0 | f) /. x1) - ((x0 | f) /. x1)).|| is V11() real ext-real Element of REAL
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of X is non empty set
K7( the carrier of CNS, the carrier of X) is set
K6(K7( the carrier of CNS, the carrier of X)) is set
f is set
x0 is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
p is V11() real ext-real Element of REAL
dom x0 is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
x0 | f is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
dom (x0 | f) is Element of K6( the carrier of CNS)
x1 is Element of the carrier of CNS
x2 is V11() real ext-real Element of REAL
x2 / p is V11() real ext-real Element of REAL
x1 is Element of the carrier of CNS
x1 - x1 is Element of the carrier of CNS
||.(x1 - x1).|| is V11() real ext-real Element of REAL
(x2 / p) * p is V11() real ext-real Element of REAL
p * ||.(x1 - x1).|| is V11() real ext-real Element of REAL
x0 /. x1 is Element of the carrier of X
x0 /. x1 is Element of the carrier of X
(x0 /. x1) - (x0 /. x1) is Element of the carrier of X
||.((x0 /. x1) - (x0 /. x1)).|| is V11() real ext-real Element of REAL
(x0 | f) /. x1 is Element of the carrier of X
((x0 | f) /. x1) - (x0 /. x1) is Element of the carrier of X
||.(((x0 | f) /. x1) - (x0 /. x1)).|| is V11() real ext-real Element of REAL
(x0 | f) /. x1 is Element of the carrier of X
((x0 | f) /. x1) - ((x0 | f) /. x1) is Element of the carrier of X
||.(((x0 | f) /. x1) - ((x0 | f) /. x1)).|| is V11() real ext-real Element of REAL
p " is V11() real ext-real Element of REAL
x1 is V11() real ext-real Element of REAL
x2 * (p ") is V11() real ext-real Element of REAL
x1 is Element of the carrier of CNS
x1 - x1 is Element of the carrier of CNS
||.(x1 - x1).|| is V11() real ext-real Element of REAL
(x0 | f) /. x1 is Element of the carrier of X
((x0 | f) /. x1) - ((x0 | f) /. x1) is Element of the carrier of X
||.(((x0 | f) /. x1) - ((x0 | f) /. x1)).|| is V11() real ext-real Element of REAL
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of X is non empty set
K7( the carrier of X, the carrier of CNS) is set
K6(K7( the carrier of X, the carrier of CNS)) is set
f is set
x0 is Relation-like the carrier of X -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of X, the carrier of CNS))
p is V11() real ext-real Element of REAL
dom x0 is Element of K6( the carrier of X)
K6( the carrier of X) is set
x0 | f is Relation-like the carrier of X -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of X, the carrier of CNS))
dom (x0 | f) is Element of K6( the carrier of X)
x1 is Element of the carrier of X
x2 is V11() real ext-real Element of REAL
x2 / p is V11() real ext-real Element of REAL
x1 is Element of the carrier of X
x1 - x1 is Element of the carrier of X
||.(x1 - x1).|| is V11() real ext-real Element of REAL
(x2 / p) * p is V11() real ext-real Element of REAL
p * ||.(x1 - x1).|| is V11() real ext-real Element of REAL
x0 /. x1 is Element of the carrier of CNS
x0 /. x1 is Element of the carrier of CNS
(x0 /. x1) - (x0 /. x1) is Element of the carrier of CNS
||.((x0 /. x1) - (x0 /. x1)).|| is V11() real ext-real Element of REAL
(x0 | f) /. x1 is Element of the carrier of CNS
((x0 | f) /. x1) - (x0 /. x1) is Element of the carrier of CNS
||.(((x0 | f) /. x1) - (x0 /. x1)).|| is V11() real ext-real Element of REAL
(x0 | f) /. x1 is Element of the carrier of CNS
((x0 | f) /. x1) - ((x0 | f) /. x1) is Element of the carrier of CNS
||.(((x0 | f) /. x1) - ((x0 | f) /. x1)).|| is V11() real ext-real Element of REAL
p " is V11() real ext-real Element of REAL
x1 is V11() real ext-real Element of REAL
x2 * (p ") is V11() real ext-real Element of REAL
x1 is Element of the carrier of X
x1 - x1 is Element of the carrier of X
||.(x1 - x1).|| is V11() real ext-real Element of REAL
(x0 | f) /. x1 is Element of the carrier of CNS
((x0 | f) /. x1) - ((x0 | f) /. x1) is Element of the carrier of CNS
||.(((x0 | f) /. x1) - ((x0 | f) /. x1)).|| is V11() real ext-real Element of REAL
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
K7( the carrier of CNS,COMPLEX) is complex-valued set
K6(K7( the carrier of CNS,COMPLEX)) is set
X is set
f is Relation-like the carrier of CNS -defined COMPLEX -valued Function-like complex-valued Element of K6(K7( the carrier of CNS,COMPLEX))
x0 is V11() real ext-real Element of REAL
dom f is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
f | X is Relation-like the carrier of CNS -defined COMPLEX -valued Function-like complex-valued Element of K6(K7( the carrier of CNS,COMPLEX))
dom (f | X) is Element of K6( the carrier of CNS)
p is Element of the carrier of CNS
x1 is V11() real ext-real Element of REAL
x1 / x0 is V11() real ext-real Element of REAL
x1 is Element of the carrier of CNS
x1 - p is Element of the carrier of CNS
||.(x1 - p).|| is V11() real ext-real Element of REAL
(x1 / x0) * x0 is V11() real ext-real Element of REAL
x0 * ||.(x1 - p).|| is V11() real ext-real Element of REAL
f /. x1 is V11() Element of COMPLEX
f /. p is V11() Element of COMPLEX
(f /. x1) - (f /. p) is V11() Element of COMPLEX
|.((f /. x1) - (f /. p)).| is V11() real ext-real Element of REAL
(f | X) /. x1 is V11() Element of COMPLEX
((f | X) /. x1) - (f /. p) is V11() Element of COMPLEX
|.(((f | X) /. x1) - (f /. p)).| is V11() real ext-real Element of REAL
(f | X) /. p is V11() Element of COMPLEX
((f | X) /. x1) - ((f | X) /. p) is V11() Element of COMPLEX
|.(((f | X) /. x1) - ((f | X) /. p)).| is V11() real ext-real Element of REAL
x0 " is V11() real ext-real Element of REAL
s9 is V11() real ext-real Element of REAL
x1 * (x0 ") is V11() real ext-real Element of REAL
x1 is Element of the carrier of CNS
x1 - p is Element of the carrier of CNS
||.(x1 - p).|| is V11() real ext-real Element of REAL
(f | X) /. x1 is V11() Element of COMPLEX
((f | X) /. x1) - ((f | X) /. p) is V11() Element of COMPLEX
|.(((f | X) /. x1) - ((f | X) /. p)).| is V11() real ext-real Element of REAL
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
K7( the carrier of CNS,REAL) is complex-valued ext-real-valued real-valued set
K6(K7( the carrier of CNS,REAL)) is set
X is set
f is Relation-like the carrier of CNS -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7( the carrier of CNS,REAL))
x0 is V11() real ext-real Element of REAL
dom f is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
f | X is Relation-like the carrier of CNS -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7( the carrier of CNS,REAL))
dom (f | X) is Element of K6( the carrier of CNS)
p is Element of the carrier of CNS
x1 is V11() real ext-real Element of REAL
x1 / x0 is V11() real ext-real Element of REAL
x1 is Element of the carrier of CNS
x1 - p is Element of the carrier of CNS
||.(x1 - p).|| is V11() real ext-real Element of REAL
(x1 / x0) * x0 is V11() real ext-real Element of REAL
x0 * ||.(x1 - p).|| is V11() real ext-real Element of REAL
f /. x1 is V11() real ext-real Element of REAL
f /. p is V11() real ext-real Element of REAL
(f /. x1) - (f /. p) is V11() real ext-real Element of REAL
abs ((f /. x1) - (f /. p)) is V11() real ext-real Element of REAL
(f | X) /. x1 is V11() real ext-real Element of REAL
((f | X) /. x1) - (f /. p) is V11() real ext-real Element of REAL
abs (((f | X) /. x1) - (f /. p)) is V11() real ext-real Element of REAL
(f | X) /. p is V11() real ext-real Element of REAL
((f | X) /. x1) - ((f | X) /. p) is V11() real ext-real Element of REAL
abs (((f | X) /. x1) - ((f | X) /. p)) is V11() real ext-real Element of REAL
x0 " is V11() real ext-real Element of REAL
s9 is V11() real ext-real Element of REAL
x1 * (x0 ") is V11() real ext-real Element of REAL
x1 is Element of the carrier of CNS
x1 - p is Element of the carrier of CNS
||.(x1 - p).|| is V11() real ext-real Element of REAL
(f | X) /. x1 is V11() real ext-real Element of REAL
((f | X) /. x1) - ((f | X) /. p) is V11() real ext-real Element of REAL
abs (((f | X) /. x1) - ((f | X) /. p)) is V11() real ext-real Element of REAL
CNS is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of CNS is non empty set
K7( the carrier of CNS,COMPLEX) is complex-valued set
K6(K7( the carrier of CNS,COMPLEX)) is set
X is set
f is Relation-like the carrier of CNS -defined COMPLEX -valued Function-like complex-valued Element of K6(K7( the carrier of CNS,COMPLEX))
x0 is V11() real ext-real Element of REAL
dom f is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
f | X is Relation-like the carrier of CNS -defined COMPLEX -valued Function-like complex-valued Element of K6(K7( the carrier of CNS,COMPLEX))
dom (f | X) is Element of K6( the carrier of CNS)
p is Element of the carrier of CNS
x1 is V11() real ext-real Element of REAL
x1 / x0 is V11() real ext-real Element of REAL
x1 is Element of the carrier of CNS
x1 - p is Element of the carrier of CNS
||.(x1 - p).|| is V11() real ext-real Element of REAL
(x1 / x0) * x0 is V11() real ext-real Element of REAL
x0 * ||.(x1 - p).|| is V11() real ext-real Element of REAL
f /. x1 is V11() Element of COMPLEX
f /. p is V11() Element of COMPLEX
(f /. x1) - (f /. p) is V11() Element of COMPLEX
|.((f /. x1) - (f /. p)).| is V11() real ext-real Element of REAL
(f | X) /. x1 is V11() Element of COMPLEX
((f | X) /. x1) - (f /. p) is V11() Element of COMPLEX
|.(((f | X) /. x1) - (f /. p)).| is V11() real ext-real Element of REAL
(f | X) /. p is V11() Element of COMPLEX
((f | X) /. x1) - ((f | X) /. p) is V11() Element of COMPLEX
|.(((f | X) /. x1) - ((f | X) /. p)).| is V11() real ext-real Element of REAL
x0 " is V11() real ext-real Element of REAL
s9 is V11() real ext-real Element of REAL
x1 * (x0 ") is V11() real ext-real Element of REAL
x1 is Element of the carrier of CNS
x1 - p is Element of the carrier of CNS
||.(x1 - p).|| is V11() real ext-real Element of REAL
(f | X) /. x1 is V11() Element of COMPLEX
((f | X) /. x1) - ((f | X) /. p) is V11() Element of COMPLEX
|.(((f | X) /. x1) - ((f | X) /. p)).| is V11() real ext-real Element of REAL
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of X is non empty set
K7( the carrier of CNS, the carrier of X) is set
K6(K7( the carrier of CNS, the carrier of X)) is set
f is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
rng f is Element of K6( the carrier of X)
K6( the carrier of X) is set
dom f is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
x0 is Element of the carrier of X
{x0} is non empty set
p is Element of the carrier of CNS
x1 is Element of the carrier of CNS
f . x1 is set
f /. x1 is Element of the carrier of X
f . p is set
f /. p is Element of the carrier of X
(f /. p) - (f /. x1) is Element of the carrier of X
||.((f /. p) - (f /. x1)).|| is V11() real ext-real Element of REAL
0. X is V97(X) Element of the carrier of X
||.(0. X).|| is V11() real ext-real Element of REAL
p - x1 is Element of the carrier of CNS
||.(p - x1).|| is V11() real ext-real Element of REAL
1 * ||.(p - x1).|| is V11() real ext-real Element of REAL
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of X is non empty set
K7( the carrier of CNS, the carrier of X) is set
K6(K7( the carrier of CNS, the carrier of X)) is set
f is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
rng f is Element of K6( the carrier of X)
K6( the carrier of X) is set
dom f is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
x0 is Element of the carrier of X
{x0} is non empty set
p is Element of the carrier of CNS
x1 is Element of the carrier of CNS
f . x1 is set
f /. x1 is Element of the carrier of X
f . p is set
f /. p is Element of the carrier of X
(f /. p) - (f /. x1) is Element of the carrier of X
||.((f /. p) - (f /. x1)).|| is V11() real ext-real Element of REAL
0. X is V97(X) Element of the carrier of X
||.(0. X).|| is V11() real ext-real Element of REAL
p - x1 is Element of the carrier of CNS
||.(p - x1).|| is V11() real ext-real Element of REAL
1 * ||.(p - x1).|| is V11() real ext-real Element of REAL
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of X is non empty set
K7( the carrier of X, the carrier of CNS) is set
K6(K7( the carrier of X, the carrier of CNS)) is set
f is Relation-like the carrier of X -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of X, the carrier of CNS))
rng f is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
dom f is Element of K6( the carrier of X)
K6( the carrier of X) is set
x0 is Element of the carrier of CNS
{x0} is non empty set
p is Element of the carrier of X
x1 is Element of the carrier of X
f . x1 is set
f /. x1 is Element of the carrier of CNS
f . p is set
f /. p is Element of the carrier of CNS
(f /. p) - (f /. x1) is Element of the carrier of CNS
||.((f /. p) - (f /. x1)).|| is V11() real ext-real Element of REAL
0. CNS is V97(CNS) Element of the carrier of CNS
||.(0. CNS).|| is V11() real ext-real Element of REAL
p - x1 is Element of the carrier of X
||.(p - x1).|| is V11() real ext-real Element of REAL
1 * ||.(p - x1).|| is V11() real ext-real Element of REAL
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of X is non empty set
K7( the carrier of CNS, the carrier of X) is set
K6(K7( the carrier of CNS, the carrier of X)) is set
f is set
x0 is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
dom x0 is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
x0 | f is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
X is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of X is non empty set
K7( the carrier of CNS, the carrier of X) is set
K6(K7( the carrier of CNS, the carrier of X)) is set
f is set
x0 is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
dom x0 is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
x0 | f is Relation-like the carrier of CNS -defined the carrier of X -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of X))
X is non empty V116() V141() V142() V143() V144() V145() V146() V147() V151() V152() RealNormSpace-like NORMSTR
the carrier of X is non empty set
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
K7( the carrier of X, the carrier of CNS) is set
K6(K7( the carrier of X, the carrier of CNS)) is set
f is set
x0 is Relation-like the carrier of X -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of X, the carrier of CNS))
dom x0 is Element of K6( the carrier of X)
K6( the carrier of X) is set
x0 | f is Relation-like the carrier of X -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of X, the carrier of CNS))
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
K7( the carrier of CNS, the carrier of CNS) is set
K6(K7( the carrier of CNS, the carrier of CNS)) is set
X is Relation-like the carrier of CNS -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of CNS))
dom X is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
f is Element of the carrier of CNS
x0 is Element of the carrier of CNS
X /. f is Element of the carrier of CNS
X /. x0 is Element of the carrier of CNS
(X /. f) - (X /. x0) is Element of the carrier of CNS
||.((X /. f) - (X /. x0)).|| is V11() real ext-real Element of REAL
f - x0 is Element of the carrier of CNS
||.(f - x0).|| is V11() real ext-real Element of REAL
1 * ||.(f - x0).|| is V11() real ext-real Element of REAL
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
K7( the carrier of CNS, the carrier of CNS) is set
K6(K7( the carrier of CNS, the carrier of CNS)) is set
X is Relation-like the carrier of CNS -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of CNS))
dom X is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
id (dom X) is Relation-like the carrier of CNS -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of CNS))
f is Element of the carrier of CNS
X /. f is Element of the carrier of CNS
X . f is set
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
K7( the carrier of CNS, the carrier of CNS) is set
K6(K7( the carrier of CNS, the carrier of CNS)) is set
K6( the carrier of CNS) is set
X is Relation-like the carrier of CNS -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of CNS))
dom X is Element of K6( the carrier of CNS)
f is Element of K6( the carrier of CNS)
X | f is Relation-like the carrier of CNS -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of CNS))
id f is Relation-like the carrier of CNS -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of CNS))
x0 is Element of the carrier of CNS
p is Element of the carrier of CNS
(dom X) /\ f is Element of K6( the carrier of CNS)
dom (X | f) is Element of K6( the carrier of CNS)
(X | f) . x0 is set
X . x0 is set
X /. x0 is Element of the carrier of CNS
(X | f) . p is set
X . p is set
X /. p is Element of the carrier of CNS
(X /. x0) - (X /. p) is Element of the carrier of CNS
||.((X /. x0) - (X /. p)).|| is V11() real ext-real Element of REAL
x0 - p is Element of the carrier of CNS
||.(x0 - p).|| is V11() real ext-real Element of REAL
1 * ||.(x0 - p).|| is V11() real ext-real Element of REAL
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
K7( the carrier of CNS, the carrier of CNS) is set
K6(K7( the carrier of CNS, the carrier of CNS)) is set
X is set
f is Relation-like the carrier of CNS -defined the carrier of CNS -valued Function-like Element of K6(K7( the carrier of CNS, the carrier of CNS))
dom f is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
x0 is V11() set
p is Element of the carrier of CNS
|.x0.| is V11() real ext-real Element of REAL
|.x0.| + 1 is V11() real ext-real Element of REAL
0 + 0 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative Element of REAL
x1 is Element of the carrier of CNS
x2 is Element of the carrier of CNS
f /. x1 is Element of the carrier of CNS
x0 * x1 is Element of the carrier of CNS
(x0 * x1) + p is Element of the carrier of CNS
f /. x2 is Element of the carrier of CNS
x0 * x2 is Element of the carrier of CNS
(x0 * x2) + p is Element of the carrier of CNS
(f /. x1) - (f /. x2) is Element of the carrier of CNS
||.((f /. x1) - (f /. x2)).|| is V11() real ext-real Element of REAL
p + (x0 * x2) is Element of the carrier of CNS
p - (p + (x0 * x2)) is Element of the carrier of CNS
(x0 * x1) + (p - (p + (x0 * x2))) is Element of the carrier of CNS
||.((x0 * x1) + (p - (p + (x0 * x2)))).|| is V11() real ext-real Element of REAL
p - p is Element of the carrier of CNS
(p - p) - (x0 * x2) is Element of the carrier of CNS
(x0 * x1) + ((p - p) - (x0 * x2)) is Element of the carrier of CNS
||.((x0 * x1) + ((p - p) - (x0 * x2))).|| is V11() real ext-real Element of REAL
0. CNS is V97(CNS) Element of the carrier of CNS
(0. CNS) - (x0 * x2) is Element of the carrier of CNS
(x0 * x1) + ((0. CNS) - (x0 * x2)) is Element of the carrier of CNS
||.((x0 * x1) + ((0. CNS) - (x0 * x2))).|| is V11() real ext-real Element of REAL
- (x0 * x2) is Element of the carrier of CNS
(x0 * x1) + (- (x0 * x2)) is Element of the carrier of CNS
||.((x0 * x1) + (- (x0 * x2))).|| is V11() real ext-real Element of REAL
(x0 * x1) - (x0 * x2) is Element of the carrier of CNS
||.((x0 * x1) - (x0 * x2)).|| is V11() real ext-real Element of REAL
x1 - x2 is Element of the carrier of CNS
x0 * (x1 - x2) is Element of the carrier of CNS
||.(x0 * (x1 - x2)).|| is V11() real ext-real Element of REAL
||.(x1 - x2).|| is V11() real ext-real Element of REAL
|.x0.| * ||.(x1 - x2).|| is V11() real ext-real Element of REAL
||.((f /. x1) - (f /. x2)).|| + 0 is V11() real ext-real Element of REAL
1 * ||.(x1 - x2).|| is V11() real ext-real Element of REAL
(|.x0.| * ||.(x1 - x2).||) + (1 * ||.(x1 - x2).||) is V11() real ext-real Element of REAL
(|.x0.| + 1) * ||.(x1 - x2).|| is V11() real ext-real Element of REAL
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
K7( the carrier of CNS,REAL) is complex-valued ext-real-valued real-valued set
K6(K7( the carrier of CNS,REAL)) is set
X is Relation-like the carrier of CNS -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7( the carrier of CNS,REAL))
dom X is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
x0 is Element of the carrier of CNS
||.x0.|| is V11() real ext-real Element of REAL
f is Element of the carrier of CNS
||.f.|| is V11() real ext-real Element of REAL
||.x0.|| - ||.f.|| is V11() real ext-real Element of REAL
x0 - f is Element of the carrier of CNS
||.(x0 - f).|| is V11() real ext-real Element of REAL
f - x0 is Element of the carrier of CNS
||.(f - x0).|| is V11() real ext-real Element of REAL
||.f.|| - ||.x0.|| is V11() real ext-real Element of REAL
- ||.(f - x0).|| is V11() real ext-real Element of REAL
- (||.f.|| - ||.x0.||) is V11() real ext-real Element of REAL
- (- (||.f.|| - ||.x0.||)) is V11() real ext-real Element of REAL
X /. f is V11() real ext-real Element of REAL
X /. x0 is V11() real ext-real Element of REAL
(X /. f) - (X /. x0) is V11() real ext-real Element of REAL
abs ((X /. f) - (X /. x0)) is V11() real ext-real Element of REAL
1 * ||.(f - x0).|| is V11() real ext-real Element of REAL
CNS is non empty V116() V141() V142() V143() V151() V152() V160() V161() V162() V163() ComplexNormSpace-like CNORMSTR
the carrier of CNS is non empty set
K7( the carrier of CNS,REAL) is complex-valued ext-real-valued real-valued set
K6(K7( the carrier of CNS,REAL)) is set
X is set
f is Relation-like the carrier of CNS -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7( the carrier of CNS,REAL))
dom f is Element of K6( the carrier of CNS)
K6( the carrier of CNS) is set
(dom f) /\ X is Element of K6( the carrier of CNS)
f | X is Relation-like the carrier of CNS -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7( the carrier of CNS,REAL))
dom (f | X) is Element of K6( the carrier of CNS)
x0 is Element of the carrier of CNS
(f | X) /. x0 is V11() real ext-real Element of REAL
f /. x0 is V11() real ext-real Element of REAL
||.x0.|| is V11() real ext-real Element of REAL