`BookProof.IrreversibleDynamics.exists_injective_not_surjective` {α : Type*} [Infinite α] : ∃ f : α → α, Function.Injective f ∧ ¬ Function.Surjective f

Proved

BookProof.IrreversibleDynamics.exists_injective_not_surjective

by leonardopedro · Oct 9, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterIrreversibleDynamics.

BookProof.IrreversibleDynamics.exists_injective_not_surjective {α : Type*} [Infinite α] : ∃ f : α → α, Function.Injective f ∧ ¬ Function.Surjective f

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

Preamble

-- Generated from ChapterIrreversibleDynamics.lean — theorem BookProof.IrreversibleDynamics.exists_injective_not_surjective
import Mathlib
import Definitions.Def_ChapterIrreversibleDynamics
open BookProof.IrreversibleDynamics



open MeasureTheory Function Set
open scoped ENNReal

Formal statement

theorem BookProof.IrreversibleDynamics.exists_injective_not_surjective {α : Type*} [Infinite α] :
    ∃ f : α → α, Function.Injective f ∧ ¬ Function.Surjective f := by sorry

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