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diff --git a/matita/matita/contribs/lambda-delta/Basic-2/reduction/cpr_lift.ma b/matita/matita/contribs/lambda-delta/Basic-2/reduction/cpr_lift.ma
index 89f84afaa..42703c24d 100644
--- a/matita/matita/contribs/lambda-delta/Basic-2/reduction/cpr_lift.ma
+++ b/matita/matita/contribs/lambda-delta/Basic-2/reduction/cpr_lift.ma
@@ -12,20 +12,44 @@
 (*                                                                        *)
 (**************************************************************************)
 
+include "Basic-2/unfold/tpss_lift.ma".
 include "Basic-2/reduction/tpr_lift.ma".
 include "Basic-2/reduction/cpr.ma".
 
 (* CONTEXT-SENSITIVE PARALLEL REDUCTION ON TERMS ****************************)
 
-(* Relocation properties ****************************************************)
-
-(* Basic-1: was: pr2_lift *)
+(* Advanced properties ******************************************************)
 
-(* Basic-1: was: pr2_gen_lift *)
+lemma cpr_delta: ∀L,K,V1,W1,W2,i.
+                 ↓[0, i] L ≡ K. 𝕓{Abbr} V1 → K ⊢ V1 [0, |L| - i - 1] ≫* W1 →
+                 ↑[0, i + 1] W1 ≡ W2 → L ⊢ #i ⇒ W2.
+#L #K #V1 #W1 #W2 #i #HLK #HVW1 #HW12
+@ex2_1_intro [2: // | skip | @tpss_subst /2 width=6/ ] (**) (* /4 width=6/ is too slow *)
+qed.
 
 (* Advanced inversion lemmas ************************************************)
 
+(* Basic-1: was: pr2_gen_lref *)
+lemma cpr_inv_lref1: ∀L,T2,i. L ⊢ #i ⇒ T2 →
+                     T2 = #i ∨
+                     ∃∃K,V1,T1. ↓[0, i] L ≡ K. 𝕓{Abbr} V1 &
+                                K ⊢ V1 [0, |L| - i - 1] ≫* T1 &
+                                ↑[0, i + 1] T1 ≡ T2 &
+                                i < |L|.
+#L #T2 #i * #X #H
+>(tpr_inv_atom1 … H) -H #H
+elim (tpss_inv_lref1 … H) -H /2/
+* /3 width=6/
+qed.
+
 (* Basic-1: was: pr2_gen_abst *)
 lemma cpr_inv_abst1: ∀V1,T1,U2. 𝕔{Abst} V1. T1 ⇒ U2 →
                      ∃∃V2,T2. V1 ⇒ V2 & T1 ⇒ T2 & U2 = 𝕔{Abst} V2. T2.
 /2/ qed.
+
+(* Relocation properties ****************************************************)
+
+(* Basic-1: was: pr2_lift *)
+
+(* Basic-1: was: pr2_gen_lift *)
+