`BookProof.ChapterLaplacianProduct.euler_clm` (L : E →L[ℝ] ℝ) (x : E) : fderiv ℝ (fun y : E => L y) x x = (1 : ℕ) * L x

Proved

BookProof.ChapterLaplacianProduct.euler_clm

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterLaplacianProduct.

BookProof.ChapterLaplacianProduct.euler_clm (L : E →L[ℝ] ℝ) (x : E) : fderiv ℝ (fun y : E => L y) x x = (1 : ℕ) * L x

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

Preamble

-- Generated from ChapterLaplacianProduct.lean — theorem BookProof.ChapterLaplacianProduct.euler_clm
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.euler_clm (L : E →L[ℝ] ℝ) (x : E) : fderiv ℝ (fun y : E => L y) x x = (1 : ℕ) * L x := by sorry

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