simple induction f.
auto.
simpl in |- *.
intro.
elim a.
intro.
elim (Xeq_dec o a0).
intros; intro H3; discriminate H3.
intros; apply H.
eauto.
Qed.

(* Specifications: *)
Lemma InDOMWhenAdd :
forall (x : X) (y : Y) (f : set (X * Y)),
set_In x (DOM (set_add XYeq_dec (x, y) f)).