proposition: Lemma lt_a_phi0_b_def : forall a b, b <_phi0 a <-> lt b (phi0 a).
proof: Proof. split. - intros; now apply lt_a_phi0_b_phi0. - intros; now apply lt_a_phi0_b_phi0R. 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)