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diff --git a/matita/matita/contribs/lambdadelta/static_2/relocation/lifts_theq.ma b/matita/matita/contribs/lambdadelta/static_2/relocation/lifts_theq.ma
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+++ b/matita/matita/contribs/lambdadelta/static_2/relocation/lifts_theq.ma
@@ -0,0 +1,70 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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 "static_2/syntax/theq.ma".
+include "static_2/relocation/lifts_lifts.ma".
+
+(* GENERIC RELOCATION FOR TERMS *********************************************)
+
+(* Properties with tail sort-irrelevant head equivalence for terms **********)
+
+lemma theq_lifts_bi: liftable2_bi theq.
+#T1 #T2 #H elim H -T1 -T2 [||| * ]
+[ #s1 #s2 #f #X1 #H1 #X2 #H2
+  >(lifts_inv_sort1 … H1) -H1 >(lifts_inv_sort1 … H2) -H2
+  /1 width=1 by theq_sort/
+| #i #f #X1 #H1 #X2 #H2
+  elim (lifts_inv_lref1 … H1) -H1 #j1 #Hj1 #H destruct
+  elim (lifts_inv_lref1 … H2) -H2 #j2 #Hj2 #H destruct
+  <(at_mono … Hj2 … Hj1) -i -f -j2
+  /1 width=1 by theq_lref/
+| #l #f #X1 #H1 #X2 #H2
+  >(lifts_inv_gref1 … H1) -H1 >(lifts_inv_gref1 … H2) -H2
+  /1 width=1 by theq_gref/
+| #p #I #V1 #V2 #T1 #T2 #f #X1 #H1 #X2 #H2
+  elim (lifts_inv_bind1 … H1) -H1 #W1 #U1 #_ #_ #H destruct
+  elim (lifts_inv_bind1 … H2) -H2 #W2 #U2 #_ #_ #H destruct
+  /1 width=1 by theq_pair/
+| #I #V1 #V2 #T1 #T2 #f #X1 #H1 #X2 #H2
+  elim (lifts_inv_flat1 … H1) -H1 #W1 #U1 #_ #_ #H destruct
+  elim (lifts_inv_flat1 … H2) -H2 #W2 #U2 #_ #_ #H destruct
+  /1 width=1 by theq_pair/
+]
+qed-.
+
+(* Inversion lemmas with tail sort-irrelevant head equivalence for terms ****)
+
+lemma theq_inv_lifts_bi: deliftable2_bi theq.
+#U1 #U2 #H elim H -U1 -U2 [||| * ]
+[ #s1 #s2 #f #X1 #H1 #X2 #H2
+  >(lifts_inv_sort2 … H1) -H1 >(lifts_inv_sort2 … H2) -H2
+  /1 width=1 by theq_sort/
+| #j #f #X1 #H1 #X2 #H2
+  elim (lifts_inv_lref2 … H1) -H1 #i1 #Hj1 #H destruct
+  elim (lifts_inv_lref2 … H2) -H2 #i2 #Hj2 #H destruct
+  <(at_inj … Hj2 … Hj1) -j -f -i1
+  /1 width=1 by theq_lref/
+| #l #f #X1 #H1 #X2 #H2
+  >(lifts_inv_gref2 … H1) -H1 >(lifts_inv_gref2 … H2) -H2
+  /1 width=1 by theq_gref/
+| #p #I #W1 #W2 #U1 #U2 #f #X1 #H1 #X2 #H2
+  elim (lifts_inv_bind2 … H1) -H1 #V1 #T1 #_ #_ #H destruct
+  elim (lifts_inv_bind2 … H2) -H2 #V2 #T2 #_ #_ #H destruct
+  /1 width=1 by theq_pair/
+| #I #W1 #W2 #U1 #U2 #f #X1 #H1 #X2 #H2
+  elim (lifts_inv_flat2 … H1) -H1 #V1 #T1 #_ #_ #H destruct
+  elim (lifts_inv_flat2 … H2) -H2 #V2 #T2 #_ #_ #H destruct
+  /1 width=1 by theq_pair/
+]
+qed-.