∀ {R : Type u_1} {M : Type u_2} [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {ι : Sort u_3}
  (U : ι → Submodule R M), (⨆ i, U i).dualAnnihilator = ⨅ i, (U i).dualAnnihilator