map_decode_iff — Mathlib

English

The Primrec₂ of the decode-bound function is equivalent to Primrec₂ f, i.e., Primrec₂ (λ a n, decode n).bind (f a) iff Primrec₂ f.

Русский

Эквивалентно: Primrec₂ (λ a n. decode n).bind (f a) эквивалентно Primrec₂ f.

LaTeX

$$$ Primrec_2 (\\lambda a n. decode β n).bind (f a) \iff Primrec_2 f$$$

Lean4

theorem map_decode_iff {f : α → β → σ} : (Primrec₂ fun a n => (@decode β _ n).map (f a)) ↔ Primrec₂ f :=
  by
  simp only [Option.map_eq_bind]
  exact bind_decode_iff.trans Primrec₂.option_some_iff

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