proposition: Lemma succ_ok alpha beta : Successor beta alpha <-> beta = succ alpha.
proof: Proof. split. - destruct alpha, beta; intro H. apply Successor_inv in H. destruct H;subst. reflexivity. - intros; subst ; apply Successor_succ. Qed.
imports: Coq(Arith Compare_dec Lia) hydras(Simple_LexProd ON_Generic ON_mult ON_Omega Compat815)