### 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

Home Index