`BookProof.NsLagrangianDet.hasDerivAt_dispField` (kv : K → Fin 3 → ℝ) (y : DIdx K → ℝ) (a : Fin 3 → ℝ) (r c : Fin 3) : HasDerivAt (fun t : ℝ => dispField kv y (a + t • (Pi.single c

Proved

BookProof.NsLagrangianDet.hasDerivAt_dispField

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNsLagrangianDetConvolution.

BookProof.NsLagrangianDet.hasDerivAt_dispField (kv : K → Fin 3 → ℝ) (y : DIdx K → ℝ) (a : Fin 3 → ℝ) (r c : Fin 3) : HasDerivAt (fun t : ℝ => dispField kv y (a + t • (Pi.single c (1 : ℝ) : Fin 3 → ℝ)) r) (dispGrad kv y a r c) 0

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

Preamble

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



open MvPolynomial Matrix

noncomputable section

variable {K : Type*} [Fintype K]

Formal statement

theorem BookProof.NsLagrangianDet.hasDerivAt_dispField (kv : K → Fin 3 → ℝ) (y : DIdx K → ℝ) (a : Fin 3 → ℝ)
    (r c : Fin 3) :
    HasDerivAt (fun t : ℝ => dispField kv y (a + t • (Pi.single c (1 : ℝ) : Fin 3 → ℝ)) r)
      (dispGrad kv y a r c) 0 := by sorry

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