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diff --git a/matita/matita/contribs/lambdadelta/ground/relocation/gr_sor_eq.ma b/matita/matita/contribs/lambdadelta/ground/relocation/gr_sor_eq.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/relocation/gr_tl_eq.ma".
+include "ground/relocation/gr_sor.ma".
+
+(* RELATIONAL UNION FOR GENERIC RELOCATION MAPS ***********************************************************)
+
+(* Properties with gr_eq *********************************************************)
+
+(*** sor_eq_repl_back1 *)
+corec lemma gr_sor_eq_repl_back_sn:
+            ∀f2,f. gr_eq_repl_back … (λf1. f1 ⋓ f2 ≘ f).
+#f2 #f #f1 * -f1 -f2 -f
+#f1 #f2 #f #g1 #g2 #g #Hf #H1 #H2 #H0 #x #Hx
+try cases (gr_eq_inv_push_sn … Hx … H1) try cases (gr_eq_inv_next_sn … Hx … H1) -g1
+/3 width=7 by gr_sor_push_bi, gr_sor_next_push, gr_sor_push_next, gr_sor_next_bi/
+qed-.
+
+(*** sor_eq_repl_fwd1 *)
+lemma gr_sor_eq_repl_fwd_sn:
+      ∀f2,f. gr_eq_repl_fwd … (λf1. f1 ⋓ f2 ≘ f).
+#f2 #f @gr_eq_repl_sym /2 width=3 by gr_sor_eq_repl_back_sn/
+qed-.
+
+(*** sor_eq_repl_back2 *)
+corec lemma gr_sor_eq_repl_back_dx:
+            ∀f1,f. gr_eq_repl_back … (λf2. f1 ⋓ f2 ≘ f).
+#f1 #f #f2 * -f1 -f2 -f
+#f1 #f2 #f #g1 #g2 #g #Hf #H #H2 #H0 #x #Hx
+try cases (gr_eq_inv_push_sn … Hx … H2) try cases (gr_eq_inv_next_sn … Hx … H2) -g2
+/3 width=7 by gr_sor_push_bi, gr_sor_next_push, gr_sor_push_next, gr_sor_next_bi/
+qed-.
+
+(*** sor_eq_repl_fwd2 *)
+lemma gr_sor_eq_repl_fwd_dx:
+      ∀f1,f. gr_eq_repl_fwd … (λf2. f1 ⋓ f2 ≘ f).
+#f1 #f @gr_eq_repl_sym /2 width=3 by gr_sor_eq_repl_back_dx/
+qed-.
+
+(*** sor_eq_repl_back3 *)
+corec lemma gr_sor_eq_repl_back:
+            ∀f1,f2. gr_eq_repl_back … (λf. f1 ⋓ f2 ≘ f).
+#f1 #f2 #f * -f1 -f2 -f
+#f1 #f2 #f #g1 #g2 #g #Hf #H #H2 #H0 #x #Hx
+try cases (gr_eq_inv_push_sn … Hx … H0) try cases (gr_eq_inv_next_sn … Hx … H0) -g
+/3 width=7 by gr_sor_push_bi, gr_sor_next_push, gr_sor_push_next, gr_sor_next_bi/
+qed-.
+
+(*** sor_eq_repl_fwd3 *)
+lemma gr_sor_eq_repl_fwd:
+      ∀f1,f2. gr_eq_repl_fwd … (λf. f1 ⋓ f2 ≘ f).
+#f1 #f2 @gr_eq_repl_sym /2 width=3 by gr_sor_eq_repl_back/
+qed-.