Prove2Me

`BookProof.ChapterAttentionMasking.causalSoftmax_eq_conditional` (beta : ℝ) (s : Fin m → ℝ) {i j : Fin m} (hij : j ≤ i) : maskedSoftmax beta s (causalMask m i) j = scoreSoftmax bet

Proved
BookProof.ChapterAttentionMasking.causalSoftmax_eq_conditional

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterAttentionMasking.

BookProof.ChapterAttentionMasking.causalSoftmax_eq_conditional (beta : ℝ) (s : Fin m → ℝ) {i j : Fin m} (hij : j ≤ i) : maskedSoftmax beta s (causalMask m i) j = scoreSoftmax beta s j / ∑ l ∈ causalMask m i, scoreSoftmax beta s l

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

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


open scoped BigOperators

noncomputable section


open BookProof.ChapterSoftmaxSharpness BookProof.ChapterSoftmaxOrder

variable {m : ℕ}
Formal statement
theorem BookProof.ChapterAttentionMasking.causalSoftmax_eq_conditional (beta : ℝ) (s : Fin m → ℝ) {i j : Fin m} (hij : j ≤ i) :
    maskedSoftmax beta s (causalMask m i) j
      = scoreSoftmax beta s j / ∑ l ∈ causalMask m i, scoreSoftmax beta s l := by sorry

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