proposition: Lemma succ_as_plus : forall alpha, nf alpha -> alpha + one = succ alpha.
proof: Proof. intro alpha;elim alpha. - cbn;auto with T2. - cbn; intros; case t; case t0. + cbn; rewrite Nat.add_0_r;auto with T2. + cbn; rewrite <- H1; cbn;auto with T2. inversion H2;auto with T2. + cbn; rewrite <- H1; cbn;auto with T2. inversion H2;auto with T2. + cbn; rewrite <- H1; cbn;auto with T2. inversion H2;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)