`BookProof.ChapterAttentionMarkov.push_sum_one` {P : Fin m → Fin m → ℝ} {p : Fin m → ℝ} (hP : IsStochastic P) (hp : ∑ j, p j = 1) : ∑ j, push P p j = 1

Proved

BookProof.ChapterAttentionMarkov.push_sum_one

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterAttentionMarkov.

BookProof.ChapterAttentionMarkov.push_sum_one {P : Fin m → Fin m → ℝ} {p : Fin m → ℝ} (hP : IsStochastic P) (hp : ∑ j, p j = 1) : ∑ j, push P p j = 1

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

Preamble

-- Generated from ChapterAttentionMarkov.lean — theorem BookProof.ChapterAttentionMarkov.push_sum_one
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_sum_one {P : Fin m → Fin m → ℝ} {p : Fin m → ℝ} (hP : IsStochastic P)
    (hp : ∑ j, p j = 1) : ∑ j, push P p j = 1 := by sorry

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