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diff --git a/matita/matita/contribs/lambdadelta/ground/relocation/gr_coafter_eq.ma b/matita/matita/contribs/lambdadelta/ground/relocation/gr_coafter_eq.ma
deleted file mode 100644
index 3d0b3c440..000000000
--- a/matita/matita/contribs/lambdadelta/ground/relocation/gr_coafter_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_coafter.ma".
-
-(* RELATIONAL CO-COMPOSITION FOR GENERIC RELOCATION MAPS ********************)
-
-(* Constructions with gr_eq *************************************************)
-
-(*** coafter_eq_repl_back2 *)
-corec lemma gr_coafter_eq_repl_back_sn:
-            ∀f1,f. gr_eq_repl_back (λf2. f2 ~⊚ f1 ≘ f).
-#f1 #f #f2 * -f2 -f1 -f
-#f21 #f1 #f #g21 [1,2: #g1 ] #g #Hf #H21 [1,2: #H1 ] #H #g22 #H0
-[ cases (gr_eq_inv_push_sn …  H0 …  H21) -g21 /3 width=7 by gr_coafter_refl/
-| cases (gr_eq_inv_push_sn …  H0 …  H21) -g21 /3 width=7 by gr_coafter_push/
-| cases (gr_eq_inv_next_sn …  H0 …  H21) -g21 /3 width=5 by gr_coafter_next/
-]
-qed-.
-
-(*** coafter_eq_repl_fwd2 *)
-lemma gr_coafter_eq_repl_fwd_sn:
-      ∀f1,f. gr_eq_repl_fwd (λf2. f2 ~⊚ f1 ≘ f).
-#f1 #f @gr_eq_repl_sym /2 width=3 by gr_coafter_eq_repl_back_sn/
-qed-.
-
-(*** coafter_eq_repl_back1 *)
-corec lemma gr_coafter_eq_repl_back_dx:
-            ∀f2,f. gr_eq_repl_back (λf1. f2 ~⊚ f1 ≘ f).
-#f2 #f #f1 * -f2 -f1 -f
-#f2 #f11 #f #g2 [1,2: #g11 ] #g #Hf #H2 [1,2: #H11 ] #H #g2 #H0
-[ cases (gr_eq_inv_push_sn …  H0 …  H11) -g11 /3 width=7 by gr_coafter_refl/
-| cases (gr_eq_inv_next_sn …  H0 …  H11) -g11 /3 width=7 by gr_coafter_push/
-| @(gr_coafter_next … H2 H) /2 width=5 by/
-]
-qed-.
-
-(*** coafter_eq_repl_fwd1 *)
-lemma gr_coafter_eq_repl_fwd_dx:
-      ∀f2,f. gr_eq_repl_fwd (λf1. f2 ~⊚ f1 ≘ f).
-#f2 #f @gr_eq_repl_sym /2 width=3 by gr_coafter_eq_repl_back_dx/
-qed-.
-
-(*** coafter_eq_repl_back0 *)
-corec lemma gr_coafter_eq_repl_back:
-            ∀f1,f2. gr_eq_repl_back (λf. f2 ~⊚ f1 ≘ f).
-#f2 #f1 #f * -f2 -f1 -f
-#f2 #f1 #f01 #g2 [1,2: #g1 ] #g01 #Hf01 #H2 [1,2: #H1 ] #H01 #g02 #H0
-[ cases (gr_eq_inv_push_sn …  H0 …  H01) -g01 /3 width=7 by gr_coafter_refl/
-| cases (gr_eq_inv_next_sn …  H0 …  H01) -g01 /3 width=7 by gr_coafter_push/
-| cases (gr_eq_inv_push_sn …  H0 …  H01) -g01 /3 width=5 by gr_coafter_next/
-]
-qed-.
-
-(*** coafter_eq_repl_fwd0 *)
-lemma gr_coafter_eq_repl_fwd:
-      ∀f2,f1. gr_eq_repl_fwd (λf. f2 ~⊚ f1 ≘ f).
-#f2 #f1 @gr_eq_repl_sym /2 width=3 by gr_coafter_eq_repl_back/
-qed-.