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diff --git a/matita/matita/contribs/lambdadelta/ground/relocation/gr_isu.ma b/matita/matita/contribs/lambdadelta/ground/relocation/gr_isu.ma
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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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 ≝
+(*** isuni_isid *)
+| gr_isu_isi (f): 𝐈❪f❫ → gr_isu f
+(*** isuni_next *)
+| gr_isu_next (f): gr_isu f → ∀g. ↑f = g → 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): 𝐔❪g❫ → ∀f. ⫯f = g → 𝐈❪f❫.
+#g * -g
+[ /2 width=3 by gr_isi_inv_push/
+| #f #_ #g #H #x #Hx destruct
+  elim (eq_inv_gr_push_next … Hx)
+]
+qed-.
+
+(*** isuni_inv_next *)
+lemma gr_isu_inv_next (g): 𝐔❪g❫ → ∀f. ↑f = g → 𝐔❪f❫.
+#g * -g #f #Hf
+[ #x #Hx elim (gr_isi_inv_next … Hf … Hx)
+| #g #H #x #Hx destruct
+  >(eq_inv_gr_next_bi … Hx) -x //
+]
+qed-.
+
+(* Basic forward lemmas *****************************************************)
+
+(*** isuni_fwd_push *)
+lemma gr_isu_fwd_push (g): 𝐔❪g❫ → ∀f. ⫯f = g → 𝐔❪f❫.
+/3 width=3 by gr_isu_inv_push, gr_isu_isi/ qed-.