`BookProof.ChapterCoherentOccupation.thermalTemperature_eq_energy_expectation` {nbar : ℝ} (h : 0 ≤ nbar) : thermalTemperature nbar = ∑' n : ℕ, ((n : ℝ) + 1 / 2) * thermalProb nbar

Proved

BookProof.ChapterCoherentOccupation.thermalTemperature_eq_energy_expectation

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterCoherentOccupation.

BookProof.ChapterCoherentOccupation.thermalTemperature_eq_energy_expectation {nbar : ℝ} (h : 0 ≤ nbar) : thermalTemperature nbar = ∑' n : ℕ, ((n : ℝ) + 1 / 2) * thermalProb nbar n

Formalization note: Lean 4 identifier BookProof.ChapterCoherentOccupation.thermalTemperature_eq_energy_expectation.

Preamble

-- Generated from ChapterCoherentOccupation.lean — theorem BookProof.ChapterCoherentOccupation.thermalTemperature_eq_energy_expectation
import Mathlib
import Definitions.Def_ChapterCoherentOccupation
import Definitions.Def_ChapterCoherentTemperature
open BookProof.ChapterCoherentTemperature
open BookProof.ChapterCoherentOccupation


noncomputable section


open Real Nat ProbabilityTheory

Formal statement

theorem BookProof.ChapterCoherentOccupation.thermalTemperature_eq_energy_expectation {nbar : ℝ} (h : 0 ≤ nbar) :
    thermalTemperature nbar = ∑' n : ℕ, ((n : ℝ) + 1 / 2) * thermalProb nbar n := by sorry

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