Prove2Me

`BookProof.ChapterAttentionMarkov.compose_isStochastic` {P Q : Fin m → Fin m → ℝ} (hP : IsStochastic P) (hQ : IsStochastic Q) : IsStochastic (compose P Q)

Proved
BookProof.ChapterAttentionMarkov.compose_isStochastic

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterAttentionMarkov.

BookProof.ChapterAttentionMarkov.compose_isStochastic {P Q : Fin m → Fin m → ℝ} (hP : IsStochastic P) (hQ : IsStochastic Q) : IsStochastic (compose P Q)

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

Preamble
-- Generated from ChapterAttentionMarkov.lean — theorem BookProof.ChapterAttentionMarkov.compose_isStochastic
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.compose_isStochastic {P Q : Fin m → Fin m → ℝ} (hP : IsStochastic P)
    (hQ : IsStochastic Q) : IsStochastic (compose P Q) := by sorry

View graph