proposition: Lemma nf_LT_right : forall alpha n beta beta', nf (cons alpha n beta) -> beta' t1< beta -> nf (cons alpha n beta').
proof: Proof. intros alpha n beta beta'; repeat rewrite nf_LT_iff. intros [H1 [H2 H3]] H4; split; auto. split. eauto with T1. apply LT_trans with beta; 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)