`BookProof.ChapterSolidHarmonic.angular_harmonic` {u v : E} (hu : ‖u‖ = 1) (hv : ‖v‖ = 1) (huv : ⟪u, v⟫_ℝ = 0) (μ : ℕ) (x : E) : (Δ (angular u v μ)) x = 0

Proved

BookProof.ChapterSolidHarmonic.angular_harmonic

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSolidHarmonic.

BookProof.ChapterSolidHarmonic.angular_harmonic {u v : E} (hu : ‖u‖ = 1) (hv : ‖v‖ = 1) (huv : ⟪u, v⟫_ℝ = 0) (μ : ℕ) (x : E) : (Δ (angular u v μ)) x = 0

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

Preamble

-- Generated from ChapterSolidHarmonic.lean — theorem BookProof.ChapterSolidHarmonic.angular_harmonic
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.angular_harmonic {u v : E} (hu : ‖u‖ = 1) (hv : ‖v‖ = 1) (huv : ⟪u, v⟫_ℝ = 0)
    (μ : ℕ) (x : E) : (Δ (angular u v μ)) x = 0 := by sorry

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