`BookProof.ChapterMaxEntropy.negMulLog_sub_eq_imp` (n : ℕ) (hn : 0 < n) {x : ℝ} (hx : 0 ≤ x) (heq : Real.negMulLog x - x * Real.log n = (n : ℝ)⁻¹ - x) : x = (n : ℝ)⁻¹

Proved

BookProof.ChapterMaxEntropy.negMulLog_sub_eq_imp

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterMaxEntropy.

BookProof.ChapterMaxEntropy.negMulLog_sub_eq_imp (n : ℕ) (hn : 0 < n) {x : ℝ} (hx : 0 ≤ x) (heq : Real.negMulLog x - x * Real.log n = (n : ℝ)⁻¹ - x) : x = (n : ℝ)⁻¹

Formalization note: Lean 4 identifier BookProof.ChapterMaxEntropy.negMulLog_sub_eq_imp.

Preamble

-- Generated from ChapterMaxEntropy.lean — theorem BookProof.ChapterMaxEntropy.negMulLog_sub_eq_imp
import Mathlib
import Definitions.Def_ChapterMaxEntropy
open BookProof.ChapterMaxEntropy


open Real BigOperators Finset


variable {α : Type*} [Fintype α]

Formal statement

theorem BookProof.ChapterMaxEntropy.negMulLog_sub_eq_imp (n : ℕ) (hn : 0 < n) {x : ℝ} (hx : 0 ≤ x)
    (heq : Real.negMulLog x - x * Real.log n = (n : ℝ)⁻¹ - x) : x = (n : ℝ)⁻¹ := by sorry

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