proposition: Lemma succ_monomorphism : forall alpha (H:nf alpha) beta (H' : nf beta), lt alpha beta <-> lt (succ alpha) (succ beta).
proof: Proof. split. - intro; now apply succ_strict_mono. - intro; now apply succ_strict_monoR. 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)