∀ (l : Type u_4) (R : Type u₂) [inst : DecidableEq l] [inst_1 : CommRing R] [inst_2 : Fintype l],
  (LieAlgebra.Orthogonal.PD l R).transpose * LieAlgebra.Orthogonal.JD l R * LieAlgebra.Orthogonal.PD l R =
    2 • LieAlgebra.Orthogonal.S l R