proposition: Lemma ren_closed_C S: ren_closed S -> ren_closed (C S).
proof: Proof. intros H delta s; unfold C in *; intros (t & [H1 H2] & H3). exists (ren delta t); split. split; eauto using ren_steps, normal_ren. intros H4. eapply H, H3. destruct t; cbn in *; intuition. Qed.
imports: Morphisms Lia Undecidability.HOU(std.std) Undecidability.HOU.calculus(prelim terms syntax semantics confluence typing order)