proposition: Lemma rtc_red_sub_ren_cap : forall k u v, red R # u v -> exists s, v = sub s (ren_cap k u).
proof: Proof. induction 1; intros. apply red_sub_ren_cap. hyp. destruct (ren_cap_intro x k). exists x0. intuition. destruct IHclos_refl_trans1. destruct IHclos_refl_trans2. subst. destruct (ren_cap_sub x0 (ren_cap k x) k). destruct H1. rewrite H1, ren_cap_idem, sub_sub. exists (sub_comp x1 x2). refl. Qed.
imports: CoLoR(LogicUtil ACalls ATrs VecUtil ListUtil NatUtil RelUtil)