Nuprl Lemma : continuous-rnexp
∀I:Interval. ∀n:ℕ. x^n continuous for x ∈ I
Proof
Definitions occuring in Statement :
continuous: f[x] continuous for x ∈ I
,
interval: Interval
,
rnexp: x^k1
,
nat: ℕ
,
all: ∀x:A. B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x]
,
implies: P
⇒ Q
,
member: t ∈ T
,
uall: ∀[x:A]. B[x]
,
so_lambda: λ2x.t[x]
,
label: ...$L... t
,
rfun: I ⟶ℝ
,
nat: ℕ
,
decidable: Dec(P)
,
or: P ∨ Q
,
uimplies: b supposing a
,
not: ¬A
,
satisfiable_int_formula: satisfiable_int_formula(fmla)
,
exists: ∃x:A. B[x]
,
false: False
,
and: P ∧ Q
,
prop: ℙ
,
so_apply: x[s]
,
rnexp: x^k1
,
ifthenelse: if b then t else f fi
,
eq_int: (i =z j)
,
btrue: tt
,
int-to-real: r(n)
,
rfun-eq: rfun-eq(I;f;g)
,
r-ap: f(x)
,
nat_plus: ℕ+
,
uiff: uiff(P;Q)
,
rev_uimplies: rev_uimplies(P;Q)
Latex:
\mforall{}I:Interval. \mforall{}n:\mBbbN{}. x\^{}n continuous for x \mmember{} I
Date html generated:
2020_05_20-PM-00_24_03
Last ObjectModification:
2020_01_02-PM-01_57_39
Theory : reals
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