`BookProof.NsLagrangianDet.volume_residual_eq` (kv : K → Fin 3 → ℝ) (y : DIdx K → ℝ) (a : Fin 3 → ℝ) : (1 + dispGrad kv y a).det - 1 = ∑ q ∈ waveSet kv, ev y (volCoef kv q) * phase

Proved

BookProof.NsLagrangianDet.volume_residual_eq

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNsLagrangianDetConvolution.

BookProof.NsLagrangianDet.volume_residual_eq (kv : K → Fin 3 → ℝ) (y : DIdx K → ℝ) (a : Fin 3 → ℝ) : (1 + dispGrad kv y a).det - 1 = ∑ q ∈ waveSet kv, ev y (volCoef kv q) * phase q a

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

Preamble

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



open MvPolynomial Matrix

noncomputable section

variable {K : Type*} [Fintype K]

Formal statement

theorem BookProof.NsLagrangianDet.volume_residual_eq (kv : K → Fin 3 → ℝ) (y : DIdx K → ℝ) (a : Fin 3 → ℝ) :
    (1 + dispGrad kv y a).det - 1 = ∑ q ∈ waveSet kv, ev y (volCoef kv q) * phase q a := by sorry

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