proposition: Lemma lt_a_phi0_b_phi0R : forall a b, lt b (phi0 a) -> b <_phi0 a.
proof: Proof. induction b. - constructor. - intro H; apply lt_a_phi0_b_inv in H; constructor; auto. Qed.
imports: Coq(Arith Max Bool Lia Compare_dec Relations Ensembles Wellfounded Bool RelationClasses Operators_Properties ArithRing Logic.Eqdep_dec) hydras(More_Arith Restriction DecPreOrder) hydras(OrdNotations)