--- /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/notation/relations/predicate_u_1.ma".
+include "ground/relocation/gr_isi.ma".
+
+(* UNIFORMITY CONDITION FOR GENERIC RELOCATION MAPS ***********************************************************)
+
+(*** isuni *)
+inductive gr_isu: predicate gr_map ā
+(*** isuni_isid *)
+| gr_isu_isi (f): šāŖfā« ā gr_isu f
+(*** isuni_next *)
+| gr_isu_next (f): gr_isu f ā āg. āf = g ā gr_isu g
+.
+
+interpretation
+ "uniformity condition (generic relocation maps)"
+ 'PredicateU f = (gr_isu f).
+
+(* Basic inversion lemmas ***************************************************)
+
+(*** isuni_inv_push *)
+lemma gr_isu_inv_push (g): šāŖgā« ā āf. ā«Æf = g ā šāŖfā«.
+#g * -g
+[ /2 width=3 by gr_isi_inv_push/
+| #f #_ #g #H #x #Hx destruct
+ elim (eq_inv_gr_push_next ā¦ Hx)
+]
+qed-.
+
+(*** isuni_inv_next *)
+lemma gr_isu_inv_next (g): šāŖgā« ā āf. āf = g ā šāŖfā«.
+#g * -g #f #Hf
+[ #x #Hx elim (gr_isi_inv_next ā¦ Hf ā¦ Hx)
+| #g #H #x #Hx destruct
+ >(eq_inv_gr_next_bi ā¦ Hx) -x //
+]
+qed-.
+
+(* Basic forward lemmas *****************************************************)
+
+(*** isuni_fwd_push *)
+lemma gr_isu_fwd_push (g): šāŖgā« ā āf. ā«Æf = g ā šāŖfā«.
+/3 width=3 by gr_isu_inv_push, gr_isu_isi/ qed-.