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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
index 12f11ae45..f98626953 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpms_drops.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpms_drops.ma
@@ -47,7 +47,7 @@ qed-.
 (* Advanced properties ******************************************************)
 
 lemma cpms_delta (n) (h) (G): ∀K,V1,V2. ⦃G,K⦄ ⊢ V1 ➡*[n,h] V2 →
-                              ∀W2. ⬆*[1] V2 ≘ W2 → ⦃G,K.ⓓV1⦄ ⊢ #0 ➡*[n,h] W2.
+                              ∀W2. ⇧*[1] V2 ≘ W2 → ⦃G,K.ⓓV1⦄ ⊢ #0 ➡*[n,h] W2.
 #n #h #G #K #V1 #V2 #H @(cpms_ind_dx … H) -V2
 [ /3 width=3 by cpm_cpms, cpm_delta/
 | #n1 #n2 #V #V2 #_ #IH #HV2 #W2 #HVW2
@@ -57,7 +57,7 @@ lemma cpms_delta (n) (h) (G): ∀K,V1,V2. ⦃G,K⦄ ⊢ V1 ➡*[n,h] V2 →
 qed.
 
 lemma cpms_ell (n) (h) (G): ∀K,V1,V2. ⦃G,K⦄ ⊢ V1 ➡*[n,h] V2 →
-                            ∀W2. ⬆*[1] V2 ≘ W2 → ⦃G,K.ⓛV1⦄ ⊢ #0 ➡*[↑n,h] W2.
+                            ∀W2. ⇧*[1] V2 ≘ W2 → ⦃G,K.ⓛV1⦄ ⊢ #0 ➡*[↑n,h] W2.
 #n #h #G #K #V1 #V2 #H @(cpms_ind_dx … H) -V2
 [ /3 width=3 by cpm_cpms, cpm_ell/
 | #n1 #n2 #V #V2 #_ #IH #HV2 #W2 #HVW2
@@ -67,7 +67,7 @@ lemma cpms_ell (n) (h) (G): ∀K,V1,V2. ⦃G,K⦄ ⊢ V1 ➡*[n,h] V2 →
 qed.
 
 lemma cpms_lref (n) (h) (I) (G): ∀K,T,i. ⦃G,K⦄ ⊢ #i ➡*[n,h] T →
-                                 ∀U. ⬆*[1] T ≘ U → ⦃G,K.ⓘ{I}⦄ ⊢ #↑i ➡*[n,h] U.
+                                 ∀U. ⇧*[1] T ≘ U → ⦃G,K.ⓘ{I}⦄ ⊢ #↑i ➡*[n,h] U.
 #n #h #I #G #K #T #i #H @(cpms_ind_dx … H) -T
 [ /3 width=3 by cpm_cpms, cpm_lref/
 | #n1 #n2 #T #T2 #_ #IH #HT2 #U2 #HTU2
@@ -91,9 +91,9 @@ qed.
 (* 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 →
+                       ∀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.
+                       ∀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
@@ -104,9 +104,9 @@ lemma cpms_delta_drops (n) (h) (G):
 qed.
 
 lemma cpms_ell_drops (n) (h) (G):
-                     ∀L,K,W,i. ⬇*[i] L ≘ K.ⓛW →
+                     ∀L,K,W,i. ⇩*[i] L ≘ K.ⓛW →
                      ∀W2. ⦃G,K⦄ ⊢ W ➡*[n,h] W2 →
-                     ∀V2. ⬆*[↑i] W2 ≘ V2 → ⦃G,L⦄ ⊢ #i ➡*[↑n,h] V2.
+                     ∀V2. ⇧*[↑i] W2 ≘ V2 → ⦃G,L⦄ ⊢ #i ➡*[↑n,h] V2.
 #n #h #G #L #K #W #i #HLK #W2 #H @(cpms_ind_dx … H) -W2
 [ /3 width=6 by cpm_cpms, cpm_ell_drops/
 | #n1 #n2 #W1 #W2 #_ #IH #HW12 #V2 #HWV2
@@ -121,10 +121,10 @@ qed.
 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.
+                            | ∃∃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 *
@@ -149,7 +149,7 @@ qed-.
 lemma cpms_inv_delta_sn (n) (h) (G) (K) (V):
       ∀T2. ⦃G,K.ⓓV⦄ ⊢ #0 ➡*[n,h] T2 →
       ∨∨ ∧∧ T2 = #0 & n = 0
-       | ∃∃V2. ⦃G,K⦄ ⊢ V ➡*[n,h] V2 & ⬆*[1] V2 ≘ T2.
+       | ∃∃V2. ⦃G,K⦄ ⊢ V ➡*[n,h] V2 & ⇧*[1] V2 ≘ T2.
 #n #h #G #K #V #T2 #H
 elim (cpms_inv_lref1_drops … H) -H *
 [ /3 width=1 by or_introl, conj/
@@ -164,7 +164,7 @@ qed-.
 lemma cpms_inv_ell_sn (n) (h) (G) (K) (V):
       ∀T2. ⦃G,K.ⓛV⦄ ⊢ #0 ➡*[n,h] T2 →
       ∨∨ ∧∧ T2 = #0 & n = 0
-       | ∃∃m,V2. ⦃G,K⦄ ⊢ V ➡*[m,h] V2 & ⬆*[1] V2 ≘ T2 & n = ↑m.
+       | ∃∃m,V2. ⦃G,K⦄ ⊢ V ➡*[m,h] V2 & ⇧*[1] V2 ≘ T2 & n = ↑m.
 #n #h #G #K #V #T2 #H
 elim (cpms_inv_lref1_drops … H) -H *
 [ /3 width=1 by or_introl, conj/
@@ -179,7 +179,7 @@ qed-.
 lemma cpms_inv_lref_sn (n) (h) (G) (I) (K):
       ∀U2,i. ⦃G,K.ⓘ{I}⦄ ⊢ #↑i ➡*[n,h] U2 →
       ∨∨ ∧∧ U2 = #↑i & n = 0
-       | ∃∃T2. ⦃G,K⦄ ⊢ #i ➡*[n,h] T2 & ⬆*[1] T2 ≘ U2.
+       | ∃∃T2. ⦃G,K⦄ ⊢ #i ➡*[n,h] T2 & ⇧*[1] T2 ≘ U2.
 #n #h #G #I #K #U2 #i #H
 elim (cpms_inv_lref1_drops … H) -H *
 [ /3 width=1 by or_introl, conj/