`BookProof.ChapterLaplacianProduct.harmonic_clm` [FiniteDimensional ℝ E] (L : E →L[ℝ] ℝ) (x : E) : (Δ fun y : E => L y) x = 0

Proved

BookProof.ChapterLaplacianProduct.harmonic_clm

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterLaplacianProduct.

BookProof.ChapterLaplacianProduct.harmonic_clm [FiniteDimensional ℝ E] (L : E →L[ℝ] ℝ) (x : E) : (Δ fun y : E => L y) x = 0

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

Preamble

-- Generated from ChapterLaplacianProduct.lean — theorem BookProof.ChapterLaplacianProduct.harmonic_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.harmonic_clm [FiniteDimensional ℝ E] (L : E →L[ℝ] ℝ) (x : E) :
    (Δ fun y : E => L y) x = 0 := by sorry

View graph