∀ {R : Type u_1} [inst : CommSemiring R] {A : Type u_2} [inst_1 : Semiring A] [inst_2 : Algebra R A]
  (x x_1 : Submodule R Aᵐᵒᵖ),
  MulOpposite.op (Submodule.comap (↑(MulOpposite.opLinearEquiv R)) (x * x_1)) =
    MulOpposite.op
      (MulOpposite.unop (MulOpposite.op (Submodule.comap (↑(MulOpposite.opLinearEquiv R)) x_1)) *
        MulOpposite.unop (MulOpposite.op (Submodule.comap (↑(MulOpposite.opLinearEquiv R)) x)))