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diff --git a/matita/matita/contribs/lambda_delta/basic_2/computation/tprs_lift.ma b/matita/matita/contribs/lambda_delta/basic_2/computation/tprs_lift.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 "basic_2/reducibility/tpr_lift.ma".
+include "basic_2/computation/tprs.ma".
+
+(* CONTEXT-FREE PARALLEL COMPUTATION ON TERMS *******************************)
+
+(* Advanced inversion lemmas ************************************************)
+
+lemma tprs_inv_abst1: ∀a,V1,T1,U2. ⓛ{a}V1. T1 ➡* U2 →
+                      ∃∃V2,T2. V1 ➡* V2 & T1 ➡* T2 & U2 = ⓛ{a}V2. T2.
+#a #V1 #T1 #U2 #H @(tprs_ind … H) -U2 /2 width=5/
+#U #U2 #_ #HU2 * #V #T #HV1 #HT1 #H destruct
+elim (tpr_inv_abst1 … HU2) -HU2 #V2 #T2 #HV2 #HT2 #H destruct /3 width=5/
+qed-.
+
+lemma tprs_inv_abst: ∀a,V1,V2,T1,T2. ⓛ{a}V1. T1 ➡* ⓛ{a}V2. T2 →
+                     V1 ➡* V2 ∧ T1 ➡* T2.
+#a #V1 #V2 #T1 #T2 #H
+elim (tprs_inv_abst1 … H) -H #V #T #HV1 #HT1 #H destruct /2 width=1/
+qed-.
+
+(* Relocation properties ****************************************************)
+
+(* Note: this was missing in basic_1 *)
+lemma tprs_lift: t_liftable tprs.
+/3 width=7/ qed.
+
+(* Note: this was missing in basic_1 *)
+lemma tprs_inv_lift1: t_deliftable_sn tprs.
+/3 width=3 by tpr_inv_lift1, t_deliftable_sn_TC/ qed-.