`BookProof.ChapterDisplacedThermalOverlap.displacedThermal_mean` (a : ℝ) (nbar : ℝ≥0) : ∫ x, x ∂(displacedThermal a nbar) = a

Proved

BookProof.ChapterDisplacedThermalOverlap.displacedThermal_mean

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterDisplacedThermalOverlap.

BookProof.ChapterDisplacedThermalOverlap.displacedThermal_mean (a : ℝ) (nbar : ℝ≥0) : ∫ x, x ∂(displacedThermal a nbar) = a

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

Preamble

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


noncomputable section

open MeasureTheory ProbabilityTheory Real
open scoped NNReal

Formal statement

theorem BookProof.ChapterDisplacedThermalOverlap.displacedThermal_mean (a : ℝ) (nbar : ℝ≥0) :
    ∫ x, x ∂(displacedThermal a nbar) = a := by sorry

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