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diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/llpr/cprs_lift.etc b/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/llpr/cprs_lift.etc
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index 000000000..27f0bb6e5
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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/reduction/llpr_ldrop.ma".
+include "basic_2/computation/cprs.ma".
+
+(* CONTEXT-SENSITIVE PARALLEL COMPUTATION ON TERMS **************************)
+
+(* Advanced properties ******************************************************)
+
+(* Note: apparently this was missing in basic_1 *)
+lemma cprs_delta: ∀G,L,K,V,V2,i.
+                  ⇩[i] L ≡ K.ⓓV → ⦃G, K⦄ ⊢ V ➡* V2 →
+                  ∀W2. ⇧[0, i + 1] V2 ≡ W2 → ⦃G, L⦄ ⊢ #i ➡* W2.
+#G #L #K #V #V2 #i #HLK #H elim H -V2 [ /3 width=6 by cpr_cprs, cpr_delta/ ]
+#V1 #V2 #_ #HV12 #IHV1 #W2 #HVW2
+lapply (ldrop_fwd_drop2 … HLK) -HLK #HLK
+elim (lift_total V1 0 (i+1)) /4 width=12 by cpr_lift, cprs_strap1/
+qed.
+
+lemma cprs_llpr_conf: ∀G. s_r_confluent1 … (cprs G) (llpr G 0).
+/3 width=5 by llpr_cpr_conf, s_r_conf1_LTC1/ qed-.
+
+(* Advanced inversion lemmas ************************************************)
+
+(* Basic_1: was: pr3_gen_lref *)
+lemma cprs_inv_lref1: ∀G,L,T2,i. ⦃G, L⦄ ⊢ #i ➡* T2 →
+                      T2 = #i ∨
+                      ∃∃K,V1,T1. ⇩[i] L ≡ K.ⓓV1 & ⦃G, K⦄ ⊢ V1 ➡* T1 &
+                                 ⇧[0, i + 1] T1 ≡ T2.
+#G #L #T2 #i #H @(cprs_ind … H) -T2 /2 width=1 by or_introl/
+#T #T2 #_ #HT2 *
+[ #H destruct
+  elim (cpr_inv_lref1 … HT2) -HT2 /2 width=1 by or_introl/
+  * /4 width=6 by cpr_cprs, ex3_3_intro, or_intror/
+| * #K #V1 #T1 #HLK #HVT1 #HT1
+  lapply (ldrop_fwd_drop2 … HLK) #H0LK
+  elim (cpr_inv_lift1 … HT2 … H0LK … HT1) -H0LK -T
+ /4 width=6 by cprs_strap1, ex3_3_intro, or_intror/
+]
+qed-.
+
+(* Relocation properties ****************************************************)
+
+(* Basic_1: was: pr3_lift *)
+lemma cprs_lift: ∀G. l_liftable (cprs G).
+/3 width=10 by l_liftable_LTC, cpr_lift/ qed.
+
+(* Basic_1: was: pr3_gen_lift *)
+lemma cprs_inv_lift1: ∀G. l_deliftable_sn (cprs G).
+/3 width=6 by l_deliftable_sn_LTC, cpr_inv_lift1/
+qed-.