Prove2Me

`BookProof.NsLagrangianDet.det_eq_one_of_volPot_eq_zero` {kappa : ℝ} (hk : 0 < kappa) (kv : K → Fin 3 → ℝ) (y : DIdx K → ℝ) (h : ev y (volPot kappa kv) = 0) (a : Fin 3 → ℝ) : (1 +

Proved
BookProof.NsLagrangianDet.det_eq_one_of_volPot_eq_zero

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNsLagrangianDetConvolution.

BookProof.NsLagrangianDet.det_eq_one_of_volPot_eq_zero {kappa : ℝ} (hk : 0 < kappa) (kv : K → Fin 3 → ℝ) (y : DIdx K → ℝ) (h : ev y (volPot kappa kv) = 0) (a : Fin 3 → ℝ) : (1 + dispGrad kv y a).det = 1

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

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



open MvPolynomial Matrix

noncomputable section

variable {K : Type*} [Fintype K]
Formal statement
theorem BookProof.NsLagrangianDet.det_eq_one_of_volPot_eq_zero {kappa : ℝ} (hk : 0 < kappa) (kv : K → Fin 3 → ℝ)
    (y : DIdx K → ℝ) (h : ev y (volPot kappa kv) = 0) (a : Fin 3 → ℝ) :
    (1 + dispGrad kv y a).det = 1 := by sorry

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