proposition: Lemma replace_all_id x : forall u, replace_all x x u = u.
proof: Proof. induction u; simpl. rewrite replace_var_id. refl. refl. rewrite IHu1, IHu2. refl. rewrite replace_var_id, IHu. refl. Qed.
imports: CoLoR(LogicUtil LAlpha RelUtil BoolUtil) Coq(Morphisms)