`BookProof.ChapterSoftmaxBorn.coherentBorn_sq_eq` (q k : EuclideanSpace ℝ (Fin n)) : bornNumer q k = Real.exp (-‖q‖ ^ 2) * Real.exp (-‖k‖ ^ 2) * Real.exp (2 * inner ℝ q k)

Proved

BookProof.ChapterSoftmaxBorn.coherentBorn_sq_eq

by leonardopedro · Oct 10, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSoftmaxBorn.

BookProof.ChapterSoftmaxBorn.coherentBorn_sq_eq (q k : EuclideanSpace ℝ (Fin n)) : bornNumer q k = Real.exp (-‖q‖ ^ 2) * Real.exp (-‖k‖ ^ 2) * Real.exp (2 * inner ℝ q k)

Formalization note: Lean 4 identifier BookProof.ChapterSoftmaxBorn.coherentBorn_sq_eq.

Preamble

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


open scoped BigOperators

noncomputable section


open BookProof.ChapterCoherentOverlap

variable {n m : ℕ}

Formal statement

theorem BookProof.ChapterSoftmaxBorn.coherentBorn_sq_eq (q k : EuclideanSpace ℝ (Fin n)) :
    bornNumer q k =
      Real.exp (-‖q‖ ^ 2) * Real.exp (-‖k‖ ^ 2) * Real.exp (2 * inner ℝ q k) := by sorry

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