`BookProof.ChapterMaxEntropy.entropy_le_entropy_uniform` [Nonempty α] {p : α → ℝ} (hp : IsProb p) : entropy p ≤ entropy (uniform α)

Proved

BookProof.ChapterMaxEntropy.entropy_le_entropy_uniform

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterMaxEntropy.

BookProof.ChapterMaxEntropy.entropy_le_entropy_uniform [Nonempty α] {p : α → ℝ} (hp : IsProb p) : entropy p ≤ entropy (uniform α)

Formalization note: Lean 4 identifier BookProof.ChapterMaxEntropy.entropy_le_entropy_uniform.

Preamble

-- Generated from ChapterMaxEntropy.lean — theorem BookProof.ChapterMaxEntropy.entropy_le_entropy_uniform
import Mathlib
import Definitions.Def_ChapterMaxEntropy
import Definitions.Def_ChapterA3n
import Definitions.Def_ChapterDutchBook
import Definitions.Def_ChapterIrreversible
open BookProof.ChapterA3n
open BookProof.ChapterDutchBook
open BookProof.ChapterIrreversible
open BookProof.ChapterMaxEntropy


open Real BigOperators Finset


variable {α : Type*} [Fintype α]

Formal statement

theorem BookProof.ChapterMaxEntropy.entropy_le_entropy_uniform [Nonempty α] {p : α → ℝ} (hp : IsProb p) :
    entropy p ≤ entropy (uniform α) := by sorry

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