`BookProof.ChapterMaxEntropy.entropy_uniform` [Nonempty α] : entropy (uniform α) = Real.log (Fintype.card α)

Proved

BookProof.ChapterMaxEntropy.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_uniform [Nonempty α] : entropy (uniform α) = Real.log (Fintype.card α)

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

Preamble

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


open Real BigOperators Finset


variable {α : Type*} [Fintype α]

Formal statement

theorem BookProof.ChapterMaxEntropy.entropy_uniform [Nonempty α] :
    entropy (uniform α) = Real.log (Fintype.card α) := by sorry

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