`BookProof.ChapterDisplacedThermalOverlap.dtOverlap_eq` (nbar : ℝ≥0) (a b : ℝ) : dtOverlap nbar a b = Real.exp (-(a - b) ^ 2 / (4 * ((nbar : ℝ) + 1 / 2))) / Real.sqrt (4 * π * ((nb

Proved

BookProof.ChapterDisplacedThermalOverlap.dtOverlap_eq

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterDisplacedThermalOverlap.

BookProof.ChapterDisplacedThermalOverlap.dtOverlap_eq (nbar : ℝ≥0) (a b : ℝ) : dtOverlap nbar a b = Real.exp (-(a - b) ^ 2 / (4 * ((nbar : ℝ) + 1 / 2))) / Real.sqrt (4 * π * ((nbar : ℝ) + 1 / 2))

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

Preamble

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


noncomputable section

open MeasureTheory ProbabilityTheory Real
open scoped NNReal

Formal statement

theorem BookProof.ChapterDisplacedThermalOverlap.dtOverlap_eq (nbar : ℝ≥0) (a b : ℝ) :
    dtOverlap nbar a b
      = Real.exp (-(a - b) ^ 2 / (4 * ((nbar : ℝ) + 1 / 2)))
        / Real.sqrt (4 * π * ((nbar : ℝ) + 1 / 2)) := by sorry

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