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`BookProof.ChapterEntropy.exists_injective_not_surjective` : ∃ f : ℕ → ℕ, Function.Injective f ∧ ¬ Function.Surjective f

Proved
BookProof.ChapterEntropy.exists_injective_not_surjective

by leonardopedro · Oct 8, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterEntropy.

BookProof.ChapterEntropy.exists_injective_not_surjective : ∃ f : ℕ → ℕ, Function.Injective f ∧ ¬ Function.Surjective f

Formalization note: Lean 4 identifier BookProof.ChapterEntropy.exists_injective_not_surjective.

Preamble
-- Generated from ChapterEntropy.lean — theorem BookProof.ChapterEntropy.exists_injective_not_surjective
import Mathlib
import Definitions.Def_ChapterEntropy
open BookProof.ChapterEntropy



open Filter Asymptotics
open scoped Topology
Formal statement
theorem BookProof.ChapterEntropy.exists_injective_not_surjective :
    ∃ f : ℕ → ℕ, Function.Injective f ∧ ¬ Function.Surjective f := by sorry

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