### Nuprl Lemma : accelerate_wf

`∀[k:ℕ+]. ∀[f:{f:ℕ+ ⟶ ℤ| k-regular-seq(f)} ].  (accelerate(k;f) ∈ ℝ)`

Proof

Definitions occuring in Statement :  accelerate: `accelerate(k;f)` real: `ℝ` regular-int-seq: `k-regular-seq(f)` nat_plus: `ℕ+` uall: `∀[x:A]. B[x]` member: `t ∈ T` set: `{x:A| B[x]} ` function: `x:A ⟶ B[x]` int: `ℤ`
Definitions unfolded in proof :  so_apply: `x[s]` so_lambda: `λ2x.t[x]` real: `ℝ` subtype_rel: `A ⊆r B` prop: `ℙ` and: `P ∧ Q` top: `Top` all: `∀x:A. B[x]` false: `False` exists: `∃x:A. B[x]` satisfiable_int_formula: `satisfiable_int_formula(fmla)` implies: `P `` Q` not: `¬A` nequal: `a ≠ b ∈ T ` nat_plus: `ℕ+` uimplies: `b supposing a` has-value: `(a)↓` accelerate: `accelerate(k;f)` member: `t ∈ T` uall: `∀[x:A]. B[x]` regular-int-seq: `k-regular-seq(f)` nat: `ℕ` squash: `↓T` true: `True` guard: `{T}` iff: `P `⇐⇒` Q` rev_implies: `P `` Q` int_nzero: `ℤ-o` sq_type: `SQType(T)` decidable: `Dec(P)` or: `P ∨ Q` sq_stable: `SqStable(P)` rev_uimplies: `rev_uimplies(P;Q)` ge: `i ≥ j ` subtract: `n - m` less_than: `a < b` le: `A ≤ B` less_than': `less_than'(a;b)`

Latex:
\mforall{}[k:\mBbbN{}\msupplus{}].  \mforall{}[f:\{f:\mBbbN{}\msupplus{}  {}\mrightarrow{}  \mBbbZ{}|  k-regular-seq(f)\}  ].    (accelerate(k;f)  \mmember{}  \mBbbR{})

Date html generated: 2020_05_20-AM-10_52_55
Last ObjectModification: 2020_03_19-PM-06_34_05

Theory : reals

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