`BookProof.ChapterMarkovEntropy.applyMarkov_permMatrix` (σ : Equiv.Perm (Fin n)) (p : Fin n → ℝ) : applyMarkov (permMatrix σ) p = fun j => p (σ.symm j)

Proved

BookProof.ChapterMarkovEntropy.applyMarkov_permMatrix

by leonardopedro · Oct 9, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterMarkovEntropy.

BookProof.ChapterMarkovEntropy.applyMarkov_permMatrix (σ : Equiv.Perm (Fin n)) (p : Fin n → ℝ) : applyMarkov (permMatrix σ) p = fun j => p (σ.symm j)

Formalization note: Lean 4 identifier BookProof.ChapterMarkovEntropy.applyMarkov_permMatrix.

Preamble

-- Generated from ChapterMarkovEntropy.lean — theorem BookProof.ChapterMarkovEntropy.applyMarkov_permMatrix
import Mathlib
import Definitions.Def_ChapterMarkovEntropy
open BookProof.ChapterMarkovEntropy


open scoped BigOperators
open Finset


variable {n : ℕ}

Formal statement

theorem BookProof.ChapterMarkovEntropy.applyMarkov_permMatrix (σ : Equiv.Perm (Fin n)) (p : Fin n → ℝ) :
    applyMarkov (permMatrix σ) p = fun j => p (σ.symm j) := by sorry

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