proposition: Lemma add_3' : forall m x y e e', ~ X.eq x y -> InA eqk (y,e) (add x e' m) -> InA eqk (y,e) m.
proof: Proof. induction m as [|[a m]]; intros x y e e' H Hm; simpl in *. - inversion_clear Hm; [|now auto]. compute in H0; elim H; auto. - destruct X.eq_dec; simpl in *. + apply InA_cons in Hm; destruct Hm; [elim H; apply X.eq_sym; apply H0|]. apply InA_cons_tl; auto. + apply InA_cons in Hm; destruct Hm; [apply InA_cons_hd; auto|]. apply InA_cons_tl; eapply IHm; eauto. Qed.
imports: FMapInterface