`BookProof.ChapterCrossEntropyGradient.crossEntropyGradient_other_nonneg` {beta : ℝ} (hb : 0 ≤ beta) (s : Fin m → ℝ) {y i : Fin m} (h : i ≠ y) : 0 ≤ crossEntropyGradient beta s y i

Proved

BookProof.ChapterCrossEntropyGradient.crossEntropyGradient_other_nonneg

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterCrossEntropyGradient.

BookProof.ChapterCrossEntropyGradient.crossEntropyGradient_other_nonneg {beta : ℝ} (hb : 0 ≤ beta) (s : Fin m → ℝ) {y i : Fin m} (h : i ≠ y) : 0 ≤ crossEntropyGradient beta s y i

Formalization note: Lean 4 identifier BookProof.ChapterCrossEntropyGradient.crossEntropyGradient_other_nonneg.

Preamble

-- Generated from ChapterCrossEntropyGradient.lean — theorem BookProof.ChapterCrossEntropyGradient.crossEntropyGradient_other_nonneg
import Definitions.Def_ChapterSoftmaxOrder
import Mathlib
import Definitions.Def_ChapterCrossEntropyGradient
import Definitions.Def_ChapterSoftmaxSharpness
open BookProof.ChapterSoftmaxSharpness
open BookProof.ChapterCrossEntropyGradient


open scoped BigOperators

noncomputable section


open BookProof.ChapterSoftmaxSharpness BookProof.ChapterSoftmaxOrder

variable {m : ℕ}

Formal statement

theorem BookProof.ChapterCrossEntropyGradient.crossEntropyGradient_other_nonneg {beta : ℝ} (hb : 0 ≤ beta) (s : Fin m → ℝ)
    {y i : Fin m} (h : i ≠ y) : 0 ≤ crossEntropyGradient beta s y i := by sorry

View graph