proposition: Lemma phi0_mono_strict : forall a b, lt a b -> lt (phi0 a) (phi0 b).
proof: Proof. auto with T1. 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)