`BookProof.ChapterCoherentGeometry.bornNumer_eq_exp_neg_dist_sq` (q k : EuclideanSpace ℝ (Fin n)) : bornNumer q k = Real.exp (-‖q - k‖ ^ 2)

Proved

BookProof.ChapterCoherentGeometry.bornNumer_eq_exp_neg_dist_sq

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterCoherentGeometry.

BookProof.ChapterCoherentGeometry.bornNumer_eq_exp_neg_dist_sq (q k : EuclideanSpace ℝ (Fin n)) : bornNumer q k = Real.exp (-‖q - k‖ ^ 2)

Formalization note: Lean 4 identifier BookProof.ChapterCoherentGeometry.bornNumer_eq_exp_neg_dist_sq.

Preamble

-- Generated from ChapterCoherentGeometry.lean — theorem BookProof.ChapterCoherentGeometry.bornNumer_eq_exp_neg_dist_sq
import Mathlib
import Definitions.Def_ChapterCoherentGeometry
import Definitions.Def_ChapterCoherentOverlap
import Definitions.Def_ChapterSoftmaxBorn
open BookProof.ChapterCoherentOverlap
open BookProof.ChapterSoftmaxBorn
open BookProof.ChapterCoherentGeometry


open scoped BigOperators

noncomputable section


open BookProof.ChapterCoherentOverlap BookProof.ChapterSoftmaxBorn

variable {n m : ℕ}

Formal statement

theorem BookProof.ChapterCoherentGeometry.bornNumer_eq_exp_neg_dist_sq (q k : EuclideanSpace ℝ (Fin n)) :
    bornNumer q k = Real.exp (-‖q - k‖ ^ 2) := by sorry

View graph