`BookProof.ChapterAttentionEntropy.shannonEntropy_uniform` (hm : 0 < m) : shannonEntropy (fun _ : Fin m => (1 : ℝ) / m) = Real.log m

Proved

BookProof.ChapterAttentionEntropy.shannonEntropy_uniform

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterAttentionEntropy.

BookProof.ChapterAttentionEntropy.shannonEntropy_uniform (hm : 0 < m) : shannonEntropy (fun _ : Fin m => (1 : ℝ) / m) = Real.log m

Formalization note: Lean 4 identifier BookProof.ChapterAttentionEntropy.shannonEntropy_uniform.

Preamble

-- Generated from ChapterAttentionEntropy.lean — theorem BookProof.ChapterAttentionEntropy.shannonEntropy_uniform
import Definitions.Def_ChapterSoftmaxBorn
import Definitions.Def_ChapterSoftmaxSharpness
import Mathlib
import Definitions.Def_ChapterAttentionEntropy
open BookProof.ChapterAttentionEntropy


open scoped BigOperators

noncomputable section


open Filter Topology BookProof.ChapterSoftmaxBorn BookProof.ChapterSoftmaxSharpness

variable {m : ℕ}

Formal statement

theorem BookProof.ChapterAttentionEntropy.shannonEntropy_uniform (hm : 0 < m) :
    shannonEntropy (fun _ : Fin m => (1 : ℝ) / m) = Real.log m := by sorry

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