`BookProof.ChapterCoherentPositionSpace.gaussianPacket_inner` (a b : ℝ) : (∫ x : ℝ, gaussianPacket a x * gaussianPacket b x) = Real.exp (-(a - b) ^ 2 / 4)

Proved

BookProof.ChapterCoherentPositionSpace.gaussianPacket_inner

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterCoherentPositionSpace.

BookProof.ChapterCoherentPositionSpace.gaussianPacket_inner (a b : ℝ) : (∫ x : ℝ, gaussianPacket a x * gaussianPacket b x) = Real.exp (-(a - b) ^ 2 / 4)

Formalization note: Lean 4 identifier BookProof.ChapterCoherentPositionSpace.gaussianPacket_inner.

Preamble

-- Generated from ChapterCoherentPositionSpace.lean — theorem BookProof.ChapterCoherentPositionSpace.gaussianPacket_inner
import Definitions.Def_ChapterCoherentOverlap
import Definitions.Def_ChapterSoftmaxSharpness
import Mathlib
import Definitions.Def_ChapterCoherentPositionSpace
open BookProof.ChapterCoherentPositionSpace


open scoped BigOperators
open MeasureTheory

noncomputable section


open BookProof.ChapterCoherentOverlap BookProof.ChapterSoftmaxSharpness

Formal statement

theorem BookProof.ChapterCoherentPositionSpace.gaussianPacket_inner (a b : ℝ) :
    (∫ x : ℝ, gaussianPacket a x * gaussianPacket b x) = Real.exp (-(a - b) ^ 2 / 4) := by sorry

View graph