`BookProof.ChapterThermalMaxEntropy.gibbs_pointwise` (h : 0 < nbar) {p : ℝ} (hp : 0 ≤ p) (n : ℕ) : p * Real.log (thermalProb nbar n) - p * Real.log p ≤ thermalProb nbar n - p

Proved

BookProof.ChapterThermalMaxEntropy.gibbs_pointwise

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterThermalMaxEntropy.

BookProof.ChapterThermalMaxEntropy.gibbs_pointwise (h : 0 < nbar) {p : ℝ} (hp : 0 ≤ p) (n : ℕ) : p * Real.log (thermalProb nbar n) - p * Real.log p ≤ thermalProb nbar n - p

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

Preamble

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


noncomputable section


open BookProof.ChapterCoherentTemperature BookProof.ChapterCoherentOccupation
open BookProof.ChapterBoseEinstein

variable {nbar : ℝ}

Formal statement

theorem BookProof.ChapterThermalMaxEntropy.gibbs_pointwise (h : 0 < nbar) {p : ℝ} (hp : 0 ≤ p) (n : ℕ) :
    p * Real.log (thermalProb nbar n) - p * Real.log p ≤ thermalProb nbar n - p := by sorry

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