`BookProof.ChapterLaplacianProduct.diffAt_fderiv` {f : E → ℝ} {x : E} (h : ContDiffAt ℝ 2 f x) : DifferentiableAt ℝ (fderiv ℝ f) x

Proved

BookProof.ChapterLaplacianProduct.diffAt_fderiv

by leonardopedro · Oct 9, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterLaplacianProduct.

BookProof.ChapterLaplacianProduct.diffAt_fderiv {f : E → ℝ} {x : E} (h : ContDiffAt ℝ 2 f x) : DifferentiableAt ℝ (fderiv ℝ f) x

Formalization note: Lean 4 identifier BookProof.ChapterLaplacianProduct.diffAt_fderiv.

Preamble

-- Generated from ChapterLaplacianProduct.lean — theorem BookProof.ChapterLaplacianProduct.diffAt_fderiv
import Definitions.Def_ChapterRadialLaplacian
import Mathlib
import Definitions.Def_ChapterLaplacianProduct
open BookProof.ChapterLaplacianProduct



open Filter Laplacian InnerProductSpace BookProof.ChapterRadialLaplacian
open scoped InnerProductSpace RealInnerProductSpace

variable {E : Type*} [NormedAddCommGroup E] [InnerProductSpace ℝ E]

Formal statement

theorem BookProof.ChapterLaplacianProduct.diffAt_fderiv {f : E → ℝ} {x : E} (h : ContDiffAt ℝ 2 f x) :
    DifferentiableAt ℝ (fderiv ℝ f) x := by sorry

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