`BookProof.ChapterAttentionMarkov.push_compose` (P Q : Fin m → Fin m → ℝ) (p : Fin m → ℝ) (j : Fin m) : push (compose P Q) p j = push Q (push P p) j

Proved

BookProof.ChapterAttentionMarkov.push_compose

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterAttentionMarkov.

BookProof.ChapterAttentionMarkov.push_compose (P Q : Fin m → Fin m → ℝ) (p : Fin m → ℝ) (j : Fin m) : push (compose P Q) p j = push Q (push P p) j

Formalization note: Lean 4 identifier BookProof.ChapterAttentionMarkov.push_compose.

Preamble

-- Generated from ChapterAttentionMarkov.lean — theorem BookProof.ChapterAttentionMarkov.push_compose
import Definitions.Def_ChapterSoftmaxSharpness
import Definitions.Def_ChapterSoftmaxOrder
import Mathlib
import Definitions.Def_ChapterAttentionMarkov
open BookProof.ChapterAttentionMarkov


open scoped BigOperators

noncomputable section


open BookProof.ChapterSoftmaxSharpness BookProof.ChapterSoftmaxOrder

variable {m : ℕ}

Formal statement

theorem BookProof.ChapterAttentionMarkov.push_compose (P Q : Fin m → Fin m → ℝ) (p : Fin m → ℝ) (j : Fin m) :
    push (compose P Q) p j = push Q (push P p) j := by sorry

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