proposition: Lemma is_compat_complete : forall R, compat R -> is_compat R = true /\ ~compat R -> is_compat R = false.
proof: Proof. induction R; simpl. intuition. destruct a. intro. ded (compat_cons_elim H). destruct H0. case (succ_dec lhs rhs); intros; destruct H2. apply IHR. exact H1. intuition. refl. Qed.
imports: CoLoR(ATrs RelUtil ListUtil ARelation SN LogicUtil)