### Nuprl Lemma : rnexp-is-positive

`∀i:ℕ+. ∀x:ℝ.  ((r0 < |x^i|) `` (r0 < |x|))`

Proof

Definitions occuring in Statement :  rless: `x < y` rabs: `|x|` rnexp: `x^k1` int-to-real: `r(n)` real: `ℝ` nat_plus: `ℕ+` all: `∀x:A. B[x]` implies: `P `` Q` natural_number: `\$n`
Definitions unfolded in proof :  all: `∀x:A. B[x]` implies: `P `` Q` member: `t ∈ T` uall: `∀[x:A]. B[x]` nat: `ℕ` le: `A ≤ B` and: `P ∧ Q` less_than': `less_than'(a;b)` not: `¬A` false: `False` uimplies: `b supposing a` iff: `P `⇐⇒` Q` prop: `ℙ` nat_plus: `ℕ+` decidable: `Dec(P)` or: `P ∨ Q` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` so_lambda: `λ2x.t[x]` so_apply: `x[s]` rless: `x < y` sq_exists: `∃x:A [B[x]]` subtype_rel: `A ⊆r B` top: `Top` sq_type: `SQType(T)` guard: `{T}` uiff: `uiff(P;Q)` ifthenelse: `if b then t else f fi ` btrue: `tt` rev_implies: `P `` Q` bfalse: `ff` squash: `↓T` less_than: `a < b`

Latex:
\mforall{}i:\mBbbN{}\msupplus{}.  \mforall{}x:\mBbbR{}.    ((r0  <  |x\^{}i|)  {}\mRightarrow{}  (r0  <  |x|))

Date html generated: 2020_05_20-AM-11_07_44
Last ObjectModification: 2019_12_14-PM-00_55_47

Theory : reals

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