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diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpms_drops.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpms_drops.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/relocation/drops_ltc.ma".
+include "basic_2/rt_transition/cpm_drops.ma".
+include "basic_2/rt_computation/cpms.ma".
+
+(* T-BOUND CONTEXT-SENSITIVE PARALLEL RT-COMPUTATION FOR TERMS **************)
+
+(* Advanced properties ******************************************************)
+
+(* Note: apparently this was missing in basic_1 *)
+(* Basic_2A1: uses: cprs_delta *)
+lemma cpms_delta_drops (n) (h) (G):
+                       ∀L,K,V,i. ⬇*[i] L ≘ K.ⓓV →
+                       ∀V2. ⦃G, K⦄ ⊢ V ➡*[n, h] V2 →
+                       ∀W2. ⬆*[↑i] V2 ≘ W2 → ⦃G, L⦄ ⊢ #i ➡*[n, h] W2.
+#n #h #G #L #K #V #i #HLK #V2 #H @(cpms_ind_dx … H) -V2
+[ /3 width=6 by cpm_cpms, cpm_delta_drops/
+| #n1 #n2 #V1 #V2 #_ #IH #HV12 #W2 #HVW2
+  lapply (drops_isuni_fwd_drop2 … HLK) -HLK // #HLK
+  elim (lifts_total V1 (𝐔❴↑i❵)) #W1 #HVW1
+  /3 width=11 by cpm_lifts_bi, cpms_step_dx/
+]
+qed.
+
+(* Advanced inversion lemmas ************************************************)
+
+lemma cpms_inv_lref1_drops (n) (h) (G):
+                           ∀L,T2,i. ⦃G, L⦄ ⊢ #i ➡*[n, h] T2 →
+                           ∨∨ ∧∧ T2 = #i & n = 0
+                            | ∃∃K,V,V2. ⬇*[i] L ≘ K.ⓓV & ⦃G, K⦄ ⊢ V ➡*[n, h] V2 &
+                                        ⬆*[↑i] V2 ≘ T2
+                            | ∃∃m,K,V,V2. ⬇*[i] L ≘ K.ⓛV & ⦃G, K⦄ ⊢ V ➡*[m, h] V2 &
+                                          ⬆*[↑i] V2 ≘ T2 & n = ↑m.
+#n #h #G #L #T2 #i #H @(cpms_ind_dx … H) -T2
+[ /3 width=1 by or3_intro0, conj/
+| #n1 #n2 #T #T2 #_ #IH #HT2 cases IH -IH *
+  [ #H1 #H2 destruct
+    elim (cpm_inv_lref1_drops … HT2) -HT2 *
+    [ /3 width=1 by or3_intro0, conj/
+    | /4 width=6 by cpm_cpms, or3_intro1, ex3_3_intro/
+    | /4 width=8 by cpm_cpms, or3_intro2, ex4_4_intro/
+    ]
+  | #K #V0 #V #HLK #HV0 #HVT
+    lapply (drops_isuni_fwd_drop2 … HLK) // #H0LK
+    elim (cpm_inv_lifts_sn … HT2 … H0LK … HVT) -H0LK -T
+    /4 width=6 by cpms_step_dx, ex3_3_intro, or3_intro1/
+  | #m #K #V0 #V #HLK #HV0 #HVT #H destruct
+    lapply (drops_isuni_fwd_drop2 … HLK) // #H0LK
+    elim (cpm_inv_lifts_sn … HT2 … H0LK … HVT) -H0LK -T
+    /4 width=8 by cpms_step_dx, ex4_4_intro, or3_intro2/
+  ]
+]
+qed-. 
+
+(* Properties with generic slicing for local environments *******************)
+
+(* Basic_2A1: uses: scpds_lift *)
+(* Basic_2A1: includes: cprs_lift *)
+(* Basic_1: includes: pr3_lift *)
+lemma cpms_lifts_sn: ∀n,h,G. d_liftable2_sn … lifts (λL. cpms h G L n).
+/3 width=6 by d2_liftable_sn_ltc, cpm_lifts_sn/ qed-.
+
+(* Inversion lemmas with generic slicing for local environments *************)
+
+(* Basic_2A1: uses: scpds_inv_lift1 *)
+(* Basic_2A1: includes: cprs_inv_lift1 *)
+(* Basic_1: includes: pr3_gen_lift *)
+lemma cpms_inv_lifts_sn: ∀n,h,G. d_deliftable2_sn … lifts (λL. cpms h G L n).
+/3 width=6 by d2_deliftable_sn_ltc, cpm_inv_lifts_sn/ qed-.