Prove2Me

`BookProof.ChapterSoftmaxDivergence.logPartition_tangent_le` (beta gamma : ℝ) (s : Fin m → ℝ) (i : Fin m) : logPartition beta s + (gamma - beta) * meanScore beta s ≤ logPartition g

Proved
BookProof.ChapterSoftmaxDivergence.logPartition_tangent_le

by leonardopedro · Oct 11, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSoftmaxDivergence.

BookProof.ChapterSoftmaxDivergence.logPartition_tangent_le (beta gamma : ℝ) (s : Fin m → ℝ) (i : Fin m) : logPartition beta s + (gamma - beta) * meanScore beta s ≤ logPartition gamma s

Formalization note: Lean 4 identifier BookProof.ChapterSoftmaxDivergence.logPartition_tangent_le.

Preamble
-- Generated from ChapterSoftmaxDivergence.lean — theorem BookProof.ChapterSoftmaxDivergence.logPartition_tangent_le
import Definitions.Def_ChapterAttentionEntropy
import Mathlib
import Definitions.Def_ChapterSoftmaxDivergence
import Definitions.Def_ChapterSoftmaxSharpness
import Definitions.Def_ChapterSoftmaxFluctuation
open BookProof.ChapterSoftmaxSharpness
open BookProof.ChapterSoftmaxDivergence


open scoped BigOperators

noncomputable section


open BookProof.ChapterAttentionEntropy BookProof.ChapterSoftmaxSharpness
open BookProof.ChapterSoftmaxFluctuation

variable {m : ℕ}
Formal statement
theorem BookProof.ChapterSoftmaxDivergence.logPartition_tangent_le (beta gamma : ℝ) (s : Fin m → ℝ) (i : Fin m) :
    logPartition beta s + (gamma - beta) * meanScore beta s ≤ logPartition gamma s := by sorry

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