--- /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_isd.ma".
+include "ground/relocation/pr_sle.ma".
+
+(* INCLUSION FOR PARTIAL RELOCATION MAPS ************************************)
+
+(* Constructions with pr_isd ************************************************)
+
+(*** sle_isdiv_dx *)
+corec lemma pr_sle_isd_dx:
+ ∀f2. 𝛀❪f2❫ → ∀f1. f1 ⊆ f2.
+#f2 * -f2
+#f2 #g2 #Hf2 #H2 #f1 cases (pr_map_split_tl f1) *
+/3 width=5 by pr_sle_weak, pr_sle_next/
+qed.
+
+(* Inversions with pr_isd ***************************************************)
+
+(*** sle_inv_isdiv_sn *)
+corec lemma pr_sle_inv_isd_sn:
+ ∀f1,f2. f1 ⊆ f2 → 𝛀❪f1❫ → 𝛀❪f2❫.
+#f1 #f2 * -f1 -f2
+#f1 #f2 #g1 #g2 #Hf * * #H
+[1,3: elim (pr_isd_inv_push … H) // ]
+lapply (pr_isd_inv_next … H ??) -H
+/3 width=3 by pr_isd_next/
+qed-.