--- /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/relocation/pr_pushs.ma".
+include "ground/relocation/pr_uni.ma".
+(* * it should not depend on pr_isi *)
+include "ground/relocation/pr_coafter_isi.ma".
+
+(* RELATIONAL CO-COMPOSITION FOR PARTIAL RELOCATION MAPS ********************)
+
+(* Constructions with pr_uni and pr_pushs ***********************************)
+
+(*** coafter_uni_sn *)
+lemma pr_coafter_uni_sn_pushs (n):
+ ∀f. 𝐮❨n❩ ~⊚ f ≘ ⫯*[n] f.
+#n @(nat_ind_succ … n) -n
+/2 width=5 by pr_coafter_isi_sn, pr_coafter_next/
+qed.