`BookProof.ChapterCoherentTemperature.thermalProb_variance` (h : 0 ≤ nbar) : (∑' n : ℕ, (n : ℝ) ^ 2 * thermalProb nbar n) - (∑' n : ℕ, (n : ℝ) * thermalProb nbar n) ^ 2 = nbar ^ 2

Proved

BookProof.ChapterCoherentTemperature.thermalProb_variance

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterCoherentTemperature.

BookProof.ChapterCoherentTemperature.thermalProb_variance (h : 0 ≤ nbar) : (∑' n : ℕ, (n : ℝ) ^ 2 * thermalProb nbar n) - (∑' n : ℕ, (n : ℝ) * thermalProb nbar n) ^ 2 = nbar ^ 2 + nbar

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

Preamble

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


noncomputable section




variable {nbar : ℝ}

Formal statement

theorem BookProof.ChapterCoherentTemperature.thermalProb_variance (h : 0 ≤ nbar) :
    (∑' n : ℕ, (n : ℝ) ^ 2 * thermalProb nbar n)
      - (∑' n : ℕ, (n : ℝ) * thermalProb nbar n) ^ 2 = nbar ^ 2 + nbar := by sorry

View graph