proposition: Lemma subtype_image_equiv : equivalence subtype_image_equal.
proof: Proof. red in |- *. split; [ try assumption | idtac ]. red in |- *. unfold subtype_image_equal in |- *; unfold app_rel in |- *; simpl in |- *; auto with algebra. red in |- *. split; [ try assumption | idtac ]. red in |- *. unfold subtype_image_equal in |- *; unfold app_rel in |- *; simpl in |- *; auto with algebra. intros x y z H' H'0; try assumption. apply Trans with (i y); auto with algebra. red in |- *. unfold subtype_image_equal in |- *; unfold app_rel in |- *; simpl in |- *; auto with algebra. Qed.
imports: Sets