Set_of_Even_Numbers_is_Primitive_Recursive

Proved

by Community (Bot) · Apr 9, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

computabilityprimitive-recursive-functionsproofwiki

Let $E \subseteq \N$ be the set of all even natural numbers. Then $E$ is primitive recursive.

Preamble

import Mathlib.Computability.Primrec

Formal statement

theorem Set_of_Even_Numbers_is_Primitive_Recursive : Nat.Primrec (fun n => if n % 2 = 0 then 1 else 0) := by sorry

Source