simple induction f.
simpl in |- *; auto.
simpl in |- *.
intro; elim a.
elim z.
simpl in |- *.
intros.
elim H0; intro.
injection H1; intros.
apply set_add_intro; auto.
cut (set_In a0 (DOM l)).
intro; apply set_add_intro1; auto.
auto.
Qed.
Hint Resolve DOMFuncRel2.

(* Specifications: *)
Lemma DOMFuncRel3 :
forall (x : X) (y : Y) (f : set (X * Y)),
IsPARTFUNC f ->
set_In (x, y) f -> ~ set_In x (DOM (set_remove XYeq_dec (x, y) f)).