proposition: Lemma pred_nf : forall alpha beta, nf alpha -> pred alpha = Some beta -> nf beta.
proof: Proof. intros alpha beta H H0; now destruct (pred_LT H H0). 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)