proposition: Lemma E0_Lt_Succ_inv (alpha beta: E0): alpha o< E0_succ beta -> alpha o< beta \/ alpha = beta.
proof: Proof. destruct alpha, beta; unfold E0lt; cbn; intros. destruct (LT_succ_LE_2 cnf_ok1 H) as [H0 [H1 H2]]. destruct H1 as [H3 |]. - left; split; auto. - subst; right; now apply E0_eq_intro. Qed.
imports: Coq(Arith Max Bool Lia Compare_dec Relations Ensembles ArithRing Wellfounded Operators_Properties Logic.Eqdep_dec) hydras(Prelude.More_Arith Prelude.Restriction Prelude.DecPreOrder ON_Generic OrdNotations)