`BookProof.ChapterBoseEinstein.boseEinstein_mean` (hx : 0 < x) : ∑' n : ℕ, (n : ℝ) * thermalProb (boseEinstein x) n = boseEinstein x

Proved

BookProof.ChapterBoseEinstein.boseEinstein_mean

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterBoseEinstein.

BookProof.ChapterBoseEinstein.boseEinstein_mean (hx : 0 < x) : ∑' n : ℕ, (n : ℝ) * thermalProb (boseEinstein x) n = boseEinstein x

Formalization note: Lean 4 identifier BookProof.ChapterBoseEinstein.boseEinstein_mean.

Preamble

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


noncomputable section

open Filter Topology


open BookProof.ChapterCoherentTemperature BookProof.ChapterCoherentOccupation

variable {x : ℝ}

Formal statement

theorem BookProof.ChapterBoseEinstein.boseEinstein_mean (hx : 0 < x) :
    ∑' n : ℕ, (n : ℝ) * thermalProb (boseEinstein x) n = boseEinstein x := by sorry

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