`BookProof.ChapterCoherentTemperature.thermalProb_mean` (h : 0 ≤ nbar) : ∑' n : ℕ, (n : ℝ) * thermalProb nbar n = nbar

Proved

BookProof.ChapterCoherentTemperature.thermalProb_mean

by leonardopedro · Oct 7, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterCoherentTemperature.

BookProof.ChapterCoherentTemperature.thermalProb_mean (h : 0 ≤ nbar) : ∑' n : ℕ, (n : ℝ) * thermalProb nbar n = nbar

Formalization note: Lean 4 identifier BookProof.ChapterCoherentTemperature.thermalProb_mean.

Preamble

-- Generated from ChapterCoherentTemperature.lean — theorem BookProof.ChapterCoherentTemperature.thermalProb_mean
import Mathlib
import Definitions.Def_ChapterCoherentTemperature
open BookProof.ChapterCoherentTemperature


noncomputable section




variable {nbar : ℝ}

Formal statement

theorem BookProof.ChapterCoherentTemperature.thermalProb_mean (h : 0 ≤ nbar) : ∑' n : ℕ, (n : ℝ) * thermalProb nbar n = nbar := by sorry

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