`BookProof.ChapterMarkovEntropy.entropy_applyMarkov_permMatrix` (σ : Equiv.Perm (Fin n)) (p : Fin n → ℝ) : entropy (applyMarkov (permMatrix σ) p) = entropy p

Proved

BookProof.ChapterMarkovEntropy.entropy_applyMarkov_permMatrix

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterMarkovEntropy.

BookProof.ChapterMarkovEntropy.entropy_applyMarkov_permMatrix (σ : Equiv.Perm (Fin n)) (p : Fin n → ℝ) : entropy (applyMarkov (permMatrix σ) p) = entropy p

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

Preamble

-- Generated from ChapterMarkovEntropy.lean — theorem BookProof.ChapterMarkovEntropy.entropy_applyMarkov_permMatrix
import Mathlib
import Definitions.Def_ChapterMarkovEntropy
import Definitions.Def_ChapterIrreversible
open BookProof.ChapterIrreversible
open BookProof.ChapterMarkovEntropy


open scoped BigOperators
open Finset


variable {n : ℕ}

Formal statement

theorem BookProof.ChapterMarkovEntropy.entropy_applyMarkov_permMatrix (σ : Equiv.Perm (Fin n)) (p : Fin n → ℝ) :
    entropy (applyMarkov (permMatrix σ) p) = entropy p := by sorry

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