∀ {R : Type u_1} {M : Type u_2} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] (W : Submodule R M)
  (φ : Module.Dual R (M ⧸ W)) (x : M), (W.dualQuotEquivDualAnnihilator φ) x = φ (Submodule.Quotient.mk x)