∀ {𝕜 : Type u_1} [inst : RCLike 𝕜] {n : Type u_2} [inst_1 : LinearOrder n] [inst_2 : WellFoundedLT n]
  [inst_3 : LocallyFiniteOrderBot n] {S : Matrix n n 𝕜} [inst_4 : Fintype n] (hS : S.PosDef) {i j : n},
  i ≠ j → inner 𝕜 (WithLp.toLp 2 (LDL.lowerInv hS i)) (WithLp.toLp 2 (S.transpose.mulVec (LDL.lowerInv hS j))) = 0