`BookProof.ChapterAttentionMasking.maskedSoftmax_le_iff` {beta : ℝ} (hbeta : 0 < beta) (s : Fin m → ℝ) {S : Finset (Fin m)} {i j : Fin m} (hi : i ∈ S) (hj : j ∈ S) : maskedSoftmax

Proved

BookProof.ChapterAttentionMasking.maskedSoftmax_le_iff

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterAttentionMasking.

BookProof.ChapterAttentionMasking.maskedSoftmax_le_iff {beta : ℝ} (hbeta : 0 < beta) (s : Fin m → ℝ) {S : Finset (Fin m)} {i j : Fin m} (hi : i ∈ S) (hj : j ∈ S) : maskedSoftmax beta s S i ≤ maskedSoftmax beta s S j ↔ s i ≤ s j

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

Preamble

-- Generated from ChapterAttentionMasking.lean — theorem BookProof.ChapterAttentionMasking.maskedSoftmax_le_iff
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_le_iff {beta : ℝ} (hbeta : 0 < beta) (s : Fin m → ℝ)
    {S : Finset (Fin m)} {i j : Fin m} (hi : i ∈ S) (hj : j ∈ S) :
    maskedSoftmax beta s S i ≤ maskedSoftmax beta s S j ↔ s i ≤ s j := by sorry

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