### Nuprl Lemma : rroot-exists-ext

`∀i:{2...}. ∀x:{x:ℝ| (↑isEven(i)) `` (r0 ≤ x)} .  (∃y:ℝ [(((↑isEven(i)) `` (r0 ≤ y)) ∧ (y^i = x))])`

Proof

Definitions occuring in Statement :  rleq: `x ≤ y` rnexp: `x^k1` req: `x = y` int-to-real: `r(n)` real: `ℝ` isEven: `isEven(n)` int_upper: `{i...}` assert: `↑b` all: `∀x:A. B[x]` sq_exists: `∃x:A [B[x]]` implies: `P `` Q` and: `P ∧ Q` set: `{x:A| B[x]} ` natural_number: `\$n`
Definitions unfolded in proof :  member: `t ∈ T` subtract: `n - m` so_lambda: `λ2x.t[x]` so_apply: `x[s]` accelerate: `accelerate(k;f)` rroot-exists rroot-exists1-ext converges-iff-cauchy rroot-exists-part2 uall: `∀[x:A]. B[x]` so_lambda: so_lambda4 so_apply: `x[s1;s2;s3;s4]` so_lambda: `λ2x y.t[x; y]` so_apply: `x[s1;s2]` uimplies: `b supposing a`

Latex:
\mforall{}i:\{2...\}.  \mforall{}x:\{x:\mBbbR{}|  (\muparrow{}isEven(i))  {}\mRightarrow{}  (r0  \mleq{}  x)\}  .    (\mexists{}y:\mBbbR{}  [(((\muparrow{}isEven(i))  {}\mRightarrow{}  (r0  \mleq{}  y))  \mwedge{}  (y\^{}i  =  x))])

Date html generated: 2020_05_20-PM-00_30_06
Last ObjectModification: 2020_03_17-PM-02_58_33

Theory : reals

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