`BookProof.SymmetryEntropy.entropy_nonneg` {p : Fin n → ℝ} (h0 : ∀ k, 0 ≤ p k) (h1 : ∀ k, p k ≤ 1) : 0 ≤ entropy p

Proved

BookProof.SymmetryEntropy.entropy_nonneg

by leonardopedro · Oct 10, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSymmetryEntropy.

BookProof.SymmetryEntropy.entropy_nonneg {p : Fin n → ℝ} (h0 : ∀ k, 0 ≤ p k) (h1 : ∀ k, p k ≤ 1) : 0 ≤ entropy p

Formalization note: Lean 4 identifier BookProof.SymmetryEntropy.entropy_nonneg.

Preamble

-- Generated from ChapterSymmetryEntropy.lean — theorem BookProof.SymmetryEntropy.entropy_nonneg
import Definitions.Def_ChapterMarkovEntropy
import Definitions.Def_ChapterReconstruct
import Mathlib
import Definitions.Def_ChapterSymmetryEntropy
import Definitions.Def_ChapterIrreversible
open BookProof.SymmetryEntropy



open Finset
open BookProof.ChapterMarkovEntropy (entropy)
open BookProof.ChapterReconstruct (IsDeterministicCol)

variable {n : ℕ}

Formal statement

theorem BookProof.SymmetryEntropy.entropy_nonneg {p : Fin n → ℝ} (h0 : ∀ k, 0 ≤ p k) (h1 : ∀ k, p k ≤ 1) :
    0 ≤ entropy p := by sorry

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