fin_val_iff — Mathlib

English

The map ULower.up : ULower α → α is primitive recursive.

Русский

Функция ULower.up : ULower α → α примитивно-рекурсивна.

LaTeX

$$$\mathrm{PR}(\mathrm{ULower}.up : \mathrm{ULower}\alpha \to \alpha)$$$

Lean4

theorem fin_val_iff {n} {f : α → Fin n} : (Primrec fun a => (f a).1) ↔ Primrec f :=
  by
  letI : Primcodable { a // id a < n } := Primcodable.subtype (nat_lt.comp .id (const _))
  exact (Iff.trans (by rfl) subtype_val_iff).trans (of_equiv_iff _)

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