`BookProof.NsLagrangianDet.one_add_dispGrad` (kv : K → Fin 3 → ℝ) (y : DIdx K → ℝ) (a : Fin 3 → ℝ) : 1 + dispGrad kv y a = Matrix.of fun r c => ∑ o : Option (SMode K), ev y (rowCoe

Proved

BookProof.NsLagrangianDet.one_add_dispGrad

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNsLagrangianDetConvolution.

BookProof.NsLagrangianDet.one_add_dispGrad (kv : K → Fin 3 → ℝ) (y : DIdx K → ℝ) (a : Fin 3 → ℝ) : 1 + dispGrad kv y a = Matrix.of fun r c => ∑ o : Option (SMode K), ev y (rowCoef kv o r c) * ophase kv a o

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

Preamble

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



open MvPolynomial Matrix

noncomputable section

variable {K : Type*} [Fintype K]

Formal statement

theorem BookProof.NsLagrangianDet.one_add_dispGrad (kv : K → Fin 3 → ℝ) (y : DIdx K → ℝ) (a : Fin 3 → ℝ) :
    1 + dispGrad kv y a
      = Matrix.of fun r c => ∑ o : Option (SMode K), ev y (rowCoef kv o r c) * ophase kv a o := by sorry

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