∀ {R : Type u} [inst : CommSemiring R] {A : Type v} [inst_1 : CommSemiring A] [inst_2 : Algebra R A]
  {s t : SetSemiring A} {M N : Submodule R A}, SetSemiring.down s ⊆ SetSemiring.down t → M ≤ N → s • M ≤ t • N