`BookProof.ChapterRadialLaplacian.hasFDerivAt_normSq` (x : E) : HasFDerivAt (fun z : E => ‖z‖ ^ 2) ((2 : ℝ) • innerCLM E x) x

Proved

BookProof.ChapterRadialLaplacian.hasFDerivAt_normSq

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterRadialLaplacian.

BookProof.ChapterRadialLaplacian.hasFDerivAt_normSq (x : E) : HasFDerivAt (fun z : E => ‖z‖ ^ 2) ((2 : ℝ) • innerCLM E x) x

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

Preamble

-- Generated from ChapterRadialLaplacian.lean — theorem BookProof.ChapterRadialLaplacian.hasFDerivAt_normSq
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.hasFDerivAt_normSq (x : E) :
    HasFDerivAt (fun z : E => ‖z‖ ^ 2) ((2 : ℝ) • innerCLM E x) x := by sorry

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