∀ {R : Type u_1} {A : Type u_2} [inst : CommSemiring R] [inst_1 : NonUnitalNonAssocSemiring A] [inst_2 : Module R A]
  {a b : NonUnitalSubalgebra R A},
  { toFun := fun S => S.toSubmodule, inj' := ⋯ } a ≤ { toFun := fun S => S.toSubmodule, inj' := ⋯ } b ↔ a ≤ b