`BookProof.ChapterThermalMaxEntropy.thermalEntropy_boseEinstein` {x : ℝ} (hx : 0 < x) : thermalEntropy (boseEinstein x) = -Real.log (1 - Real.exp (-x)) + x * boseEinstein x

Proved

BookProof.ChapterThermalMaxEntropy.thermalEntropy_boseEinstein

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterThermalMaxEntropy.

BookProof.ChapterThermalMaxEntropy.thermalEntropy_boseEinstein {x : ℝ} (hx : 0 < x) : thermalEntropy (boseEinstein x) = -Real.log (1 - Real.exp (-x)) + x * boseEinstein x

Formalization note: Lean 4 identifier BookProof.ChapterThermalMaxEntropy.thermalEntropy_boseEinstein.

Preamble

-- Generated from ChapterThermalMaxEntropy.lean — theorem BookProof.ChapterThermalMaxEntropy.thermalEntropy_boseEinstein
import Definitions.Def_ChapterCoherentOccupation
import Mathlib
import Definitions.Def_ChapterThermalMaxEntropy
import Definitions.Def_ChapterBoseEinstein
import Definitions.Def_ChapterCoherentTemperature
open BookProof.ChapterBoseEinstein
open BookProof.ChapterCoherentTemperature
open BookProof.ChapterThermalMaxEntropy


noncomputable section


open BookProof.ChapterCoherentTemperature BookProof.ChapterCoherentOccupation
open BookProof.ChapterBoseEinstein

variable {nbar : ℝ}

Formal statement

theorem BookProof.ChapterThermalMaxEntropy.thermalEntropy_boseEinstein {x : ℝ} (hx : 0 < x) :
    thermalEntropy (boseEinstein x)
      = -Real.log (1 - Real.exp (-x)) + x * boseEinstein x := by sorry

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