--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||M|| *)
+(* ||A|| A project by Andrea Asperti *)
+(* ||T|| *)
+(* ||I|| Developers: *)
+(* ||T|| The HELM team. *)
+(* ||A|| http://helm.cs.unibo.it *)
+(* \ / *)
+(* \ / This file is distributed under the terms of the *)
+(* v GNU General Public License Version 2 *)
+(* *)
+(**************************************************************************)
+
+include "ground/arith/nat_rplus_succ.ma".
+include "ground/relocation/pr_uni.ma".
+include "ground/relocation/pr_pat_pat_id.ma".
+
+(* POSITIVE APPLICATION FOR PARTIAL RELOCATION MAPS *************************)
+
+(* Constructions with pr_uni ************************************************)
+
+(*** at_uni *)
+lemma pr_pat_uni (n) (i):
+ @❪i,𝐮❨n❩❫ ≘ i+n.
+#n @(nat_ind_succ … n) -n
+/2 width=5 by pr_pat_next/
+qed.
+
+(* Inversions with pr_uni ***************************************************)
+
+(*** at_inv_uni *)
+lemma pr_pat_inv_uni (n) (i) (j):
+ @❪i,𝐮❨n❩❫ ≘ j → j = i+n.
+/2 width=4 by pr_pat_mono/ qed-.