Prove2Me

`BookProof.ChapterNote68AllModes.inner_stdVec` {i j : Fin 3} (h : i ≠ j) : ⟪stdVec i, stdVec j⟫_ℝ = 0

Proved
BookProof.ChapterNote68AllModes.inner_stdVec

by leonardopedro · Oct 6, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNote68AllModes.

BookProof.ChapterNote68AllModes.inner_stdVec {i j : Fin 3} (h : i ≠ j) : ⟪stdVec i, stdVec j⟫_ℝ = 0

Formalization note: Lean 4 identifier BookProof.ChapterNote68AllModes.inner_stdVec.

Preamble
-- Generated from ChapterNote68AllModes.lean — theorem BookProof.ChapterNote68AllModes.inner_stdVec
import Definitions.Def_ChapterSphericalBessel
import Definitions.Def_ChapterBesselHarmonic
import Definitions.Def_ChapterSolidHarmonic
import Mathlib
import Definitions.Def_ChapterNote68AllModes
open BookProof.ChapterNote68AllModes

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



open Laplacian InnerProductSpace Polynomial
open BookProof.ChapterSphericalBessel BookProof.ChapterBesselHarmonic
open BookProof.ChapterSolidHarmonic
open scoped RealInnerProductSpace
Formal statement
theorem BookProof.ChapterNote68AllModes.inner_stdVec {i j : Fin 3} (h : i ≠ j) : ⟪stdVec i, stdVec j⟫_ℝ = 0 := by sorry

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