proposition: Lemma rho_evaluates: forall x y : X, evaluates R x y -> exists n : nat, it n rho x = y.
proof: Proof. Proof using H1 H2 S tf. intros x y [H3 H4]. eapply sandwich_equiv with (S := S) in H3; eauto. eapply tak_cofinal in H3; eauto. destruct H3 as [n H3]; exists n. eapply sandwich_equiv with (S := S) in H3; eauto. now eapply Normal_star_stops in H3. Qed.
imports: Morphisms FinFun ConstructiveEpsilon Undecidability.HOU(std.tactics std.decidable std.misc std.ars.basic std.ars.confluence)