proposition: Lemma pred_of_succ : forall alpha, nf alpha -> pred (succ alpha) = Some alpha.
proof: Proof. induction alpha;cbn. - trivial. - case alpha1;case alpha2. + cbn. inversion_clear 1;auto with T2. inversion H0. inversion H5. inversion H4. inversion H12. inversion H4. inversion H4. + cbn. intros;rewrite IHalpha3. auto with T2. inversion H;auto with T2. + cbn; intros;rewrite IHalpha3. reflexivity. inversion H;auto with T2. + cbn; intros;rewrite IHalpha3; trivial. inversion H;auto with T2. Qed.
imports: Coq(Arith List Lia Compare_dec Relations Wellfounded RelationClasses) hydras(Epsilon0) hydras(More_Arith Restriction) hydras(ON_Generic) hydras(rpo.term rpo.rpo) hydras(T2) hydras(Compat815)