`BookProof.ChapterSolidHarmonic.solidHarmonicIm_euler` (u v e : E) {l μ : ℕ} (hμ : μ ≤ l) (x : E) : fderiv ℝ (solidHarmonicIm u v e l μ) x x = (l : ℝ) * solidHarmonicIm u v e l μ x

Proved

BookProof.ChapterSolidHarmonic.solidHarmonicIm_euler

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSolidHarmonic.

BookProof.ChapterSolidHarmonic.solidHarmonicIm_euler (u v e : E) {l μ : ℕ} (hμ : μ ≤ l) (x : E) : fderiv ℝ (solidHarmonicIm u v e l μ) x x = (l : ℝ) * solidHarmonicIm u v e l μ x

Formalization note: Lean 4 identifier BookProof.ChapterSolidHarmonic.solidHarmonicIm_euler.

Preamble

-- Generated from ChapterSolidHarmonic.lean — theorem BookProof.ChapterSolidHarmonic.solidHarmonicIm_euler
import Definitions.Def_ChapterRadialLaplacian
import Definitions.Def_ChapterLaplacianProduct
import Definitions.Def_ChapterSolidHarmonicTools
import Definitions.Def_ChapterLegendrePolynomial
import Mathlib
import Definitions.Def_ChapterSolidHarmonic
open BookProof.ChapterSolidHarmonic



open Laplacian InnerProductSpace Polynomial
open BookProof.ChapterRadialLaplacian BookProof.ChapterLaplacianProduct
open BookProof.ChapterSolidHarmonicTools BookProof.ChapterLegendrePolynomial
open scoped RealInnerProductSpace

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

Formal statement

theorem BookProof.ChapterSolidHarmonic.solidHarmonicIm_euler (u v e : E) {l μ : ℕ} (hμ : μ ≤ l) (x : E) :
    fderiv ℝ (solidHarmonicIm u v e l μ) x x = (l : ℝ) * solidHarmonicIm u v e l μ x := by sorry

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