`BookProof.ChapterDisplacedThermalOverlap.displacedThermal_variance` (a : ℝ) (nbar : ℝ≥0) : Var[id; displacedThermal a nbar] = (nbar : ℝ) + 1 / 2

Proved

BookProof.ChapterDisplacedThermalOverlap.displacedThermal_variance

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterDisplacedThermalOverlap.

BookProof.ChapterDisplacedThermalOverlap.displacedThermal_variance (a : ℝ) (nbar : ℝ≥0) : Var[id; displacedThermal a nbar] = (nbar : ℝ) + 1 / 2

Formalization note: Lean 4 identifier BookProof.ChapterDisplacedThermalOverlap.displacedThermal_variance.

Preamble

-- Generated from ChapterDisplacedThermalOverlap.lean — theorem BookProof.ChapterDisplacedThermalOverlap.displacedThermal_variance
import Mathlib
import Definitions.Def_ChapterDisplacedThermalOverlap
open BookProof.ChapterDisplacedThermalOverlap


noncomputable section

open MeasureTheory ProbabilityTheory Real
open scoped NNReal

Formal statement

theorem BookProof.ChapterDisplacedThermalOverlap.displacedThermal_variance (a : ℝ) (nbar : ℝ≥0) :
    Var[id; displacedThermal a nbar] = (nbar : ℝ) + 1 / 2 := by sorry

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