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

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



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

noncomputable section

variable {d : ℕ}

theorem BookProof.QuadraticRotation.inner_pgLp_rotPoly {O : Matrix (Fin d) (Fin d) ℝ} (hO : Oᵀ * O = 1)
    (p q : MvPolynomial (Fin d) ℂ) :
    (inner ℂ (pgLp (rotPoly O p)) (pgLp (rotPoly O q)) : ℂ)
      = (inner ℂ (pgLp p) (pgLp q) : ℂ) := by sorry