The Lean 4 theorem `span_rotHermiteLp` in the `ChapterQuadraticRotationEsa` chapter of the timepiece formalization

-- Generated from ChapterQuadraticRotationEsa.lean — theorem BookProof.QuadraticRotation.span_rotHermiteLp
import Definitions.Def_ChapterFarisLavine
import Definitions.Def_ChapterNavierStokesDifferentialL2
import Definitions.Def_ChapterHyperbolicQuadraticEsa
import Mathlib
import Definitions.Def_ChapterQuadraticRotationEsa
import Definitions.Def_ChapterHermiteProductBasis
import Definitions.Def_ChapterHermiteProductCore
import Definitions.Def_ChapterA4
open BookProof.HermiteProductBasis
open BookProof.HermiteProductCore
open BookProof.QuadraticRotation

variable {d : ℕ}



open MeasureTheory MvPolynomial Matrix
open BookProof.HermiteProductCore BookProof.HermiteProductBasis
open BookProof.FarisLavine
open BookProof.NavierStokesFlow.DifferentialL2
open BookProof.HyperbolicQuadratic

noncomputable section

theorem BookProof.QuadraticRotation.span_rotHermiteLp {O : Matrix (Fin d) (Fin d) ℝ} (hO : Oᵀ * O = 1) :
    Submodule.span ℂ (Set.range (rotHermiteLp (d := d) O)) = polyGaussCore (d := d) := by sorry