`BookProof.ChapterCoherentOccupation.coherentOccupation_variance` (lam : ℝ) : (∑' n : ℕ, (n : ℝ) ^ 2 * coherentOccupation lam n) - (∑' n : ℕ, (n : ℝ) * coherentOccupation lam n) ^

Proved

BookProof.ChapterCoherentOccupation.coherentOccupation_variance

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterCoherentOccupation.

BookProof.ChapterCoherentOccupation.coherentOccupation_variance (lam : ℝ) : (∑' n : ℕ, (n : ℝ) ^ 2 * coherentOccupation lam n) - (∑' n : ℕ, (n : ℝ) * coherentOccupation lam n) ^ 2 = lam

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

Preamble

-- Generated from ChapterCoherentOccupation.lean — theorem BookProof.ChapterCoherentOccupation.coherentOccupation_variance
import Mathlib
import Definitions.Def_ChapterCoherentOccupation
open BookProof.ChapterCoherentOccupation


noncomputable section


open Real Nat ProbabilityTheory

Formal statement

theorem BookProof.ChapterCoherentOccupation.coherentOccupation_variance (lam : ℝ) :
    (∑' n : ℕ, (n : ℝ) ^ 2 * coherentOccupation lam n)
      - (∑' n : ℕ, (n : ℝ) * coherentOccupation lam n) ^ 2 = lam := by sorry

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