Nuprl Lemma : continuous-rnexp2
∀I:Interval. ∀f:I ⟶ℝ. (f[x] continuous for x ∈ I ⇒ (∀n:ℕ. f[x]^n continuous for x ∈ I))
Proof
Definitions occuring in Statement :
continuous: f[x] continuous for x ∈ I,
rfun: I ⟶ℝ,
interval: Interval,
rnexp: x^k1,
nat: ℕ,
so_apply: x[s],
all: ∀x:A. B[x],
implies: P ⇒ Q
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{}f:I {}\mrightarrow{}\mBbbR{}. (f[x] continuous for x \mmember{} I {}\mRightarrow{} (\mforall{}n:\mBbbN{}. f[x]\^{}n continuous for x \mmember{} I))
Date html generated:
2020_05_20-PM-00_24_26
Last ObjectModification:
2020_01_02-PM-01_59_08
Theory : reals
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