`BookProof.ChapterRadialLaplacian.diffAt_deriv_of_contDiffAt_two` {G : ℝ → ℝ} {q : ℝ} (h : ContDiffAt ℝ 2 G q) : DifferentiableAt ℝ (deriv G) q

Proved

BookProof.ChapterRadialLaplacian.diffAt_deriv_of_contDiffAt_two

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterRadialLaplacian.

BookProof.ChapterRadialLaplacian.diffAt_deriv_of_contDiffAt_two {G : ℝ → ℝ} {q : ℝ} (h : ContDiffAt ℝ 2 G q) : DifferentiableAt ℝ (deriv G) q

Formalization note: Lean 4 identifier BookProof.ChapterRadialLaplacian.diffAt_deriv_of_contDiffAt_two.

Preamble

-- Generated from ChapterRadialLaplacian.lean — theorem BookProof.ChapterRadialLaplacian.diffAt_deriv_of_contDiffAt_two
import Mathlib
import Definitions.Def_ChapterRadialLaplacian
open BookProof.ChapterRadialLaplacian



open Filter Laplacian InnerProductSpace
open scoped InnerProductSpace RealInnerProductSpace

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

Formal statement

theorem BookProof.ChapterRadialLaplacian.diffAt_deriv_of_contDiffAt_two {G : ℝ → ℝ} {q : ℝ} (h : ContDiffAt ℝ 2 G q) :
    DifferentiableAt ℝ (deriv G) q := by sorry

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