∀ {R : Type u_1} {M : Type u_2} [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
  (U : Submodule R (Module.Dual R M)), U.dualCoannihilator.dualAnnihilator.dualCoannihilator = U.dualCoannihilator