Prove2Me

`BookProof.ChapterAttentionMixture.shannonEntropy_eq_sum_negMulLog` (p : Fin m → ℝ) : shannonEntropy p = ∑ j, Real.negMulLog (p j)

Proved
BookProof.ChapterAttentionMixture.shannonEntropy_eq_sum_negMulLog

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterAttentionMixture.

BookProof.ChapterAttentionMixture.shannonEntropy_eq_sum_negMulLog (p : Fin m → ℝ) : shannonEntropy p = ∑ j, Real.negMulLog (p j)

Formalization note: Lean 4 identifier BookProof.ChapterAttentionMixture.shannonEntropy_eq_sum_negMulLog.

Preamble
-- Generated from ChapterAttentionMixture.lean — theorem BookProof.ChapterAttentionMixture.shannonEntropy_eq_sum_negMulLog
import Definitions.Def_ChapterSoftmaxSharpness
import Definitions.Def_ChapterSoftmaxOrder
import Mathlib
import Definitions.Def_ChapterAttentionMixture
import Definitions.Def_ChapterAttentionEntropy
open BookProof.ChapterAttentionMixture


open scoped BigOperators

noncomputable section


open BookProof.ChapterSoftmaxSharpness BookProof.ChapterSoftmaxOrder
open BookProof.ChapterAttentionEntropy

variable {m H : ℕ} {E : Type*} [NormedAddCommGroup E] [NormedSpace ℝ E]
Formal statement
theorem BookProof.ChapterAttentionMixture.shannonEntropy_eq_sum_negMulLog (p : Fin m → ℝ) :
    shannonEntropy p = ∑ j, Real.negMulLog (p j) := by sorry

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