proposition: Lemma T1_to_T2_monoR : forall c c', lt (T1_to_T2 c) (T1_to_T2 c') -> T1.lt c c'.
proof: Proof. intros c c' H; case (T1.lt_eq_lt_dec c c'). - destruct 1; auto. subst c'; case (lt_irr H). - intro l; generalize (T1_to_T2_mono l); intro H0; case (lt_irr (alpha:=T1_to_T2 c)). eapply lt_trans;eauto with T2. Qed.
imports: Coq(Arith List Lia Compare_dec Relations Wellfounded RelationClasses) hydras(Epsilon0) hydras(More_Arith Restriction) hydras(ON_Generic) hydras(rpo.term rpo.rpo) hydras(T2) hydras(Compat815)