`BookProof.ChapterAttentionMasking.maskedSoftmax_restrict` (beta : ℝ) (s : Fin m → ℝ) {S T : Finset (Fin m)} (hTS : T ⊆ S) {j : Fin m} (hj : j ∈ T) : maskedSoftmax beta s T j = mas

Proved

BookProof.ChapterAttentionMasking.maskedSoftmax_restrict

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterAttentionMasking.

BookProof.ChapterAttentionMasking.maskedSoftmax_restrict (beta : ℝ) (s : Fin m → ℝ) {S T : Finset (Fin m)} (hTS : T ⊆ S) {j : Fin m} (hj : j ∈ T) : maskedSoftmax beta s T j = maskedSoftmax beta s S j / ∑ l ∈ T, maskedSoftmax beta s S l

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

Preamble

-- Generated from ChapterAttentionMasking.lean — theorem BookProof.ChapterAttentionMasking.maskedSoftmax_restrict
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_restrict (beta : ℝ) (s : Fin m → ℝ) {S T : Finset (Fin m)}
    (hTS : T ⊆ S) {j : Fin m} (hj : j ∈ T) :
    maskedSoftmax beta s T j
      = maskedSoftmax beta s S j / ∑ l ∈ T, maskedSoftmax beta s S l := by sorry

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