proposition: Lemma eq_succ_lt : forall alpha beta, nf beta -> alpha = succ beta -> lt beta alpha.
proof: Proof. intros alpha beta H H0; destruct (eq_succ_LT H H0); tauto. 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)