`BookProof.ChapterAttentionMasking.maskedSoftmax_nonneg` (beta : ℝ) (s : Fin m → ℝ) (S : Finset (Fin m)) (j : Fin m) : 0 ≤ maskedSoftmax beta s S j

Proved

BookProof.ChapterAttentionMasking.maskedSoftmax_nonneg

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterAttentionMasking.

BookProof.ChapterAttentionMasking.maskedSoftmax_nonneg (beta : ℝ) (s : Fin m → ℝ) (S : Finset (Fin m)) (j : Fin m) : 0 ≤ maskedSoftmax beta s S j

Formalization note: Lean 4 identifier BookProof.ChapterAttentionMasking.maskedSoftmax_nonneg.

Preamble

-- Generated from ChapterAttentionMasking.lean — theorem BookProof.ChapterAttentionMasking.maskedSoftmax_nonneg
import Definitions.Def_ChapterSoftmaxSharpness
import Definitions.Def_ChapterSoftmaxOrder
import Mathlib
import Definitions.Def_ChapterAttentionMasking
open BookProof.ChapterAttentionMasking


open scoped BigOperators

noncomputable section


open BookProof.ChapterSoftmaxSharpness BookProof.ChapterSoftmaxOrder

variable {m : ℕ}

Formal statement

theorem BookProof.ChapterAttentionMasking.maskedSoftmax_nonneg (beta : ℝ) (s : Fin m → ℝ) (S : Finset (Fin m)) (j : Fin m) :
    0 ≤ maskedSoftmax beta s S j := by sorry

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