`BookProof.ChapterCoherentOverlapComplex.coherentBornC_cancel_q` (q : EuclideanSpace ℂ (Fin n)) (k : Fin m → EuclideanSpace ℂ (Fin n)) (j : Fin m) : bornWeightC q k j = Real.exp (-

Proved

BookProof.ChapterCoherentOverlapComplex.coherentBornC_cancel_q

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterCoherentOverlapComplex.

BookProof.ChapterCoherentOverlapComplex.coherentBornC_cancel_q (q : EuclideanSpace ℂ (Fin n)) (k : Fin m → EuclideanSpace ℂ (Fin n)) (j : Fin m) : bornWeightC q k j = Real.exp (-‖k j‖ ^ 2) * Real.exp (2 * (inner ℂ q (k j) : ℂ).re) / ∑ l, Real.exp (-‖k l‖ ^ 2) * Real.exp (2 * (inner ℂ q (k l) : ℂ).re)

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

Preamble

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


open scoped BigOperators

noncomputable section


variable {n m : ℕ}

Formal statement

theorem BookProof.ChapterCoherentOverlapComplex.coherentBornC_cancel_q (q : EuclideanSpace ℂ (Fin n))
    (k : Fin m → EuclideanSpace ℂ (Fin n)) (j : Fin m) :
    bornWeightC q k j =
      Real.exp (-‖k j‖ ^ 2) * Real.exp (2 * (inner ℂ q (k j) : ℂ).re) /
        ∑ l, Real.exp (-‖k l‖ ^ 2) * Real.exp (2 * (inner ℂ q (k l) : ℂ).re) := by sorry

View graph