`BookProof.ChapterCoherentOverlapComplex.bornNumerC_eq` (q k : EuclideanSpace ℂ (Fin n)) : bornNumerC q k = Real.exp (-‖q‖ ^ 2) * Real.exp (-‖k‖ ^ 2) * Real.exp (2 * (inner ℂ q k :

Proved

BookProof.ChapterCoherentOverlapComplex.bornNumerC_eq

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterCoherentOverlapComplex.

BookProof.ChapterCoherentOverlapComplex.bornNumerC_eq (q k : EuclideanSpace ℂ (Fin n)) : bornNumerC q k = Real.exp (-‖q‖ ^ 2) * Real.exp (-‖k‖ ^ 2) * Real.exp (2 * (inner ℂ q k : ℂ).re)

Formalization note: Lean 4 identifier BookProof.ChapterCoherentOverlapComplex.bornNumerC_eq.

Preamble

-- Generated from ChapterCoherentOverlapComplex.lean — theorem BookProof.ChapterCoherentOverlapComplex.bornNumerC_eq
import Mathlib
import Definitions.Def_ChapterCoherentOverlapComplex
open BookProof.ChapterCoherentOverlapComplex


open scoped BigOperators

noncomputable section


variable {n m : ℕ}

Formal statement

theorem BookProof.ChapterCoherentOverlapComplex.bornNumerC_eq (q k : EuclideanSpace ℂ (Fin n)) :
    bornNumerC q k =
      Real.exp (-‖q‖ ^ 2) * Real.exp (-‖k‖ ^ 2)
        * Real.exp (2 * (inner ℂ q k : ℂ).re) := by sorry

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