proposition: Lemma diff_move : forall T eq, forall l1 l2 l3 : list T, forall x, diff eq (l1 ++ x :: l2) l3 = diff eq (x :: l1 ++ l2) l3.
proof: Proof. induction l1; simpl; sp. rewrite IHl1; simpl. rewrite remove_comm; auto. Qed.
imports: UsefulTypes bin_rels Omega