`BookProof.ChapterDisplacedThermalMulti.dtOverlapMulti_eq` (nbar : ℝ≥0) (a b : EuclideanSpace ℝ (Fin n)) : dtOverlapMulti nbar a b = Real.exp (-‖a - b‖ ^ 2 / (4 * ((nbar : ℝ) + 1 /

Proved

BookProof.ChapterDisplacedThermalMulti.dtOverlapMulti_eq

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterDisplacedThermalMulti.

BookProof.ChapterDisplacedThermalMulti.dtOverlapMulti_eq (nbar : ℝ≥0) (a b : EuclideanSpace ℝ (Fin n)) : dtOverlapMulti nbar a b = Real.exp (-‖a - b‖ ^ 2 / (4 * ((nbar : ℝ) + 1 / 2))) / (Real.sqrt (4 * π * ((nbar : ℝ) + 1 / 2))) ^ n

Formalization note: Lean 4 identifier BookProof.ChapterDisplacedThermalMulti.dtOverlapMulti_eq.

Preamble

-- Generated from ChapterDisplacedThermalMulti.lean — theorem BookProof.ChapterDisplacedThermalMulti.dtOverlapMulti_eq
import Mathlib
import Definitions.Def_ChapterDisplacedThermalMulti
import Definitions.Def_ChapterDisplacedThermalOverlap
import Definitions.Def_ChapterHermiteProductCore
open BookProof.ChapterDisplacedThermalOverlap
open BookProof.HermiteProductCore
open BookProof.ChapterDisplacedThermalMulti


noncomputable section

open MeasureTheory ProbabilityTheory Real
open scoped NNReal


open BookProof.ChapterDisplacedThermalOverlap

variable {n m : ℕ}

Formal statement

theorem BookProof.ChapterDisplacedThermalMulti.dtOverlapMulti_eq (nbar : ℝ≥0) (a b : EuclideanSpace ℝ (Fin n)) :
    dtOverlapMulti nbar a b
      = Real.exp (-‖a - b‖ ^ 2 / (4 * ((nbar : ℝ) + 1 / 2)))
        / (Real.sqrt (4 * π * ((nbar : ℝ) + 1 / 2))) ^ n := by sorry

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