`BookProof.ChapterLogPartitionConvex.strictConvexOn_logPartition` {s : Fin m → ℝ} {a b : Fin m} (hab : s a ≠ s b) : StrictConvexOn ℝ Set.univ fun c : ℝ => logPartition c s

Proved

BookProof.ChapterLogPartitionConvex.strictConvexOn_logPartition

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterLogPartitionConvex.

BookProof.ChapterLogPartitionConvex.strictConvexOn_logPartition {s : Fin m → ℝ} {a b : Fin m} (hab : s a ≠ s b) : StrictConvexOn ℝ Set.univ fun c : ℝ => logPartition c s

Formalization note: Lean 4 identifier BookProof.ChapterLogPartitionConvex.strictConvexOn_logPartition.

Preamble

-- Generated from ChapterLogPartitionConvex.lean — theorem BookProof.ChapterLogPartitionConvex.strictConvexOn_logPartition
import Definitions.Def_ChapterAttentionEntropy
import Definitions.Def_ChapterSoftmaxSharpness
import Mathlib
import Definitions.Def_ChapterLogPartitionConvex
import Definitions.Def_ChapterSoftmaxFluctuation
open BookProof.ChapterLogPartitionConvex


open scoped BigOperators

noncomputable section


open BookProof.ChapterAttentionEntropy BookProof.ChapterSoftmaxSharpness
open BookProof.ChapterSoftmaxFluctuation

variable {m : ℕ}

Formal statement

theorem BookProof.ChapterLogPartitionConvex.strictConvexOn_logPartition {s : Fin m → ℝ} {a b : Fin m} (hab : s a ≠ s b) :
    StrictConvexOn ℝ Set.univ fun c : ℝ => logPartition c s := by sorry

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