`BookProof.SymmetryEntropy.negMulLog_eq_zero_iff` {x : ℝ} (h0 : 0 ≤ x) (h1 : x ≤ 1) : Real.negMulLog x = 0 ↔ x = 0 ∨ x = 1

Proved

BookProof.SymmetryEntropy.negMulLog_eq_zero_iff

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSymmetryEntropy.

BookProof.SymmetryEntropy.negMulLog_eq_zero_iff {x : ℝ} (h0 : 0 ≤ x) (h1 : x ≤ 1) : Real.negMulLog x = 0 ↔ x = 0 ∨ x = 1

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

Preamble

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



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

variable {n : ℕ}

Formal statement

theorem BookProof.SymmetryEntropy.negMulLog_eq_zero_iff {x : ℝ} (h0 : 0 ≤ x) (h1 : x ≤ 1) :
    Real.negMulLog x = 0 ↔ x = 0 ∨ x = 1 := by sorry

View graph