`BookProof.NsLagrangianDet.ev_volPot` (kappa : ℝ) (kv : K → Fin 3 → ℝ) (y : DIdx K → ℝ) : ev y (volPot kappa kv) = ((kappa / 2 * ∑ q ∈ waveSet kv, Complex.normSq (ev y (volCoef kv

Proved

BookProof.NsLagrangianDet.ev_volPot

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNsLagrangianDetConvolution.

BookProof.NsLagrangianDet.ev_volPot (kappa : ℝ) (kv : K → Fin 3 → ℝ) (y : DIdx K → ℝ) : ev y (volPot kappa kv) = ((kappa / 2 * ∑ q ∈ waveSet kv, Complex.normSq (ev y (volCoef kv q)) : ℝ) : ℂ)

Formalization note: Lean 4 identifier BookProof.NsLagrangianDet.ev_volPot.

Preamble

-- Generated from ChapterNsLagrangianDetConvolution.lean — theorem BookProof.NsLagrangianDet.ev_volPot
import Mathlib
import Definitions.Def_ChapterNsLagrangianDetConvolution
open BookProof.NsLagrangianDet



open MvPolynomial Matrix

noncomputable section

variable {K : Type*} [Fintype K]

Formal statement

theorem BookProof.NsLagrangianDet.ev_volPot (kappa : ℝ) (kv : K → Fin 3 → ℝ) (y : DIdx K → ℝ) :
    ev y (volPot kappa kv)
      = ((kappa / 2 * ∑ q ∈ waveSet kv, Complex.normSq (ev y (volCoef kv q)) : ℝ) : ℂ) := by sorry

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