`BookProof.ComputableScarcity.exists_infinitely_often_ne` (e : ℕ → (ℕ → ℕ)) : ∃ f : ℕ → ℕ, ∀ k, {n | f n ≠ e k n}.Infinite

Proved

BookProof.ComputableScarcity.exists_infinitely_often_ne

by leonardopedro · Oct 7, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterComputableScarcity.

BookProof.ComputableScarcity.exists_infinitely_often_ne (e : ℕ → (ℕ → ℕ)) : ∃ f : ℕ → ℕ, ∀ k, {n | f n ≠ e k n}.Infinite

Formalization note: Lean 4 identifier BookProof.ComputableScarcity.exists_infinitely_often_ne.

Preamble

-- Generated from ChapterComputableScarcity.lean — theorem BookProof.ComputableScarcity.exists_infinitely_often_ne
import Mathlib
import Definitions.Def_ChapterComputableScarcity
open BookProof.ComputableScarcity



open Nat.Partrec

open Classical

Formal statement

theorem BookProof.ComputableScarcity.exists_infinitely_often_ne (e : ℕ → (ℕ → ℕ)) :
    ∃ f : ℕ → ℕ, ∀ k, {n | f n ≠ e k n}.Infinite := by sorry

View graph