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diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx.ma
index 3ba500020..5fe697558 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx.ma
@@ -28,11 +28,11 @@ interpretation
 (* Basic eliminators ********************************************************)
 
 lemma csx_ind: ∀h,o,G,L. ∀R:predicate term.
-               (∀T1. ⦃G, L⦄ ⊢ ⬈[h, o] 𝐒⦃T1⦄ →
+               (∀T1. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T1⦄ →
                      (∀T2. ⦃G, L⦄ ⊢ T1 ⬈[h] T2 → (T1 ≡[h, o] T2 → ⊥) → R T2) →
                      R T1
                ) →
-               ∀T. ⦃G, L⦄ ⊢ ⬈[h, o] 𝐒⦃T⦄ → R T.
+               ∀T. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T⦄ → R T.
 #h #o #G #L #R #H0 #T1 #H elim H -T1
 /5 width=1 by SN_intro/
 qed-.
@@ -41,11 +41,11 @@ qed-.
 
 (* Basic_1: was just: sn3_pr2_intro *)
 lemma csx_intro: ∀h,o,G,L,T1.
-                 (∀T2. ⦃G, L⦄ ⊢ T1 ⬈[h] T2 → (T1 ≡[h, o] T2 → ⊥) → ⦃G, L⦄ ⊢ ⬈[h, o] 𝐒⦃T2⦄) →
-                 ⦃G, L⦄ ⊢ ⬈[h, o] 𝐒⦃T1⦄.
+                 (∀T2. ⦃G, L⦄ ⊢ T1 ⬈[h] T2 → (T1 ≡[h, o] T2 → ⊥) → ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T2⦄) →
+                 ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T1⦄.
 /4 width=1 by SN_intro/ qed.
 
-lemma csx_sort: ∀h,o,G,L,s. ⦃G, L⦄ ⊢ ⬈[h, o] 𝐒⦃⋆s⦄.
+lemma csx_sort: ∀h,o,G,L,s. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃⋆s⦄.
 #h #o #G #L #s elim (deg_total h o s)
 #d generalize in match s; -s elim d -d
 [ #s1 #Hs1 @csx_intro #X #H #HX elim HX -HX
@@ -60,8 +60,8 @@ qed.
 
 (* Basic forward lemmas *****************************************************)
 
-fact csx_fwd_pair_sn_aux: ∀h,o,G,L,U. ⦃G, L⦄ ⊢ ⬈[h, o] 𝐒⦃U⦄ →
-                          ∀I,V,T. U = ②{I}V.T → ⦃G, L⦄ ⊢ ⬈[h, o] 𝐒⦃V⦄.
+fact csx_fwd_pair_sn_aux: ∀h,o,G,L,U. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃U⦄ →
+                          ∀I,V,T. U = ②{I}V.T → ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃V⦄.
 #h #o #G #L #U #H elim H -H #U0 #_ #IH #I #V #T #H destruct
 @csx_intro #V2 #HLV2 #HV2
 @(IH (②{I}V2.T)) -IH /2 width=3 by cpx_pair_sn/ -HLV2
@@ -69,11 +69,11 @@ fact csx_fwd_pair_sn_aux: ∀h,o,G,L,U. ⦃G, L⦄ ⊢ ⬈[h, o] 𝐒⦃U⦄ →
 qed-.
 
 (* Basic_1: was just: sn3_gen_head *)
-lemma csx_fwd_pair_sn: ∀h,o,I,G,L,V,T. ⦃G, L⦄ ⊢ ⬈[h, o] 𝐒⦃②{I}V.T⦄ → ⦃G, L⦄ ⊢ ⬈[h, o] 𝐒⦃V⦄.
+lemma csx_fwd_pair_sn: ∀h,o,I,G,L,V,T. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃②{I}V.T⦄ → ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃V⦄.
 /2 width=5 by csx_fwd_pair_sn_aux/ qed-.
 
-fact csx_fwd_bind_dx_aux: ∀h,o,G,L,U. ⦃G, L⦄ ⊢ ⬈[h, o] 𝐒⦃U⦄ →
-                          ∀p,I,V,T. U = ⓑ{p,I}V.T → ⦃G, L.ⓑ{I}V⦄ ⊢ ⬈[h, o] 𝐒⦃T⦄.
+fact csx_fwd_bind_dx_aux: ∀h,o,G,L,U. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃U⦄ →
+                          ∀p,I,V,T. U = ⓑ{p,I}V.T → ⦃G, L.ⓑ{I}V⦄ ⊢ ⬈*[h, o] 𝐒⦃T⦄.
 #h #o #G #L #U #H elim H -H #U0 #_ #IH #p #I #V #T #H destruct
 @csx_intro #T2 #HLT2 #HT2
 @(IH (ⓑ{p,I}V.T2)) -IH /2 width=3 by cpx_bind/ -HLT2
@@ -81,11 +81,11 @@ fact csx_fwd_bind_dx_aux: ∀h,o,G,L,U. ⦃G, L⦄ ⊢ ⬈[h, o] 𝐒⦃U⦄ →
 qed-.
 
 (* Basic_1: was just: sn3_gen_bind *)
-lemma csx_fwd_bind_dx: ∀h,o,p,I,G,L,V,T. ⦃G, L⦄ ⊢ ⬈[h, o] 𝐒⦃ⓑ{p,I}V.T⦄ → ⦃G, L.ⓑ{I}V⦄ ⊢ ⬈[h, o] 𝐒⦃T⦄.
+lemma csx_fwd_bind_dx: ∀h,o,p,I,G,L,V,T. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃ⓑ{p,I}V.T⦄ → ⦃G, L.ⓑ{I}V⦄ ⊢ ⬈*[h, o] 𝐒⦃T⦄.
 /2 width=4 by csx_fwd_bind_dx_aux/ qed-.
 
-fact csx_fwd_flat_dx_aux: ∀h,o,G,L,U. ⦃G, L⦄ ⊢ ⬈[h, o] 𝐒⦃U⦄ →
-                          ∀I,V,T. U = ⓕ{I}V.T → ⦃G, L⦄ ⊢ ⬈[h, o] 𝐒⦃T⦄.
+fact csx_fwd_flat_dx_aux: ∀h,o,G,L,U. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃U⦄ →
+                          ∀I,V,T. U = ⓕ{I}V.T → ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T⦄.
 #h #o #G #L #U #H elim H -H #U0 #_ #IH #I #V #T #H destruct
 @csx_intro #T2 #HLT2 #HT2
 @(IH (ⓕ{I}V.T2)) -IH /2 width=3 by cpx_flat/ -HLT2
@@ -93,15 +93,15 @@ fact csx_fwd_flat_dx_aux: ∀h,o,G,L,U. ⦃G, L⦄ ⊢ ⬈[h, o] 𝐒⦃U⦄ →
 qed-.
 
 (* Basic_1: was just: sn3_gen_flat *)
-lemma csx_fwd_flat_dx: ∀h,o,I,G,L,V,T. ⦃G, L⦄ ⊢ ⬈[h, o] 𝐒⦃ⓕ{I}V.T⦄ → ⦃G, L⦄ ⊢ ⬈[h, o] 𝐒⦃T⦄.
+lemma csx_fwd_flat_dx: ∀h,o,I,G,L,V,T. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃ⓕ{I}V.T⦄ → ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T⦄.
 /2 width=5 by csx_fwd_flat_dx_aux/ qed-.
 
-lemma csx_fwd_bind: ∀h,o,p,I,G,L,V,T. ⦃G, L⦄ ⊢ ⬈[h, o] 𝐒⦃ⓑ{p,I}V.T⦄ →
-                    ⦃G, L⦄ ⊢ ⬈[h, o] 𝐒⦃V⦄ ∧ ⦃G, L.ⓑ{I}V⦄ ⊢ ⬈[h, o] 𝐒⦃T⦄.
+lemma csx_fwd_bind: ∀h,o,p,I,G,L,V,T. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃ⓑ{p,I}V.T⦄ →
+                    ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃V⦄ ∧ ⦃G, L.ⓑ{I}V⦄ ⊢ ⬈*[h, o] 𝐒⦃T⦄.
 /3 width=3 by csx_fwd_pair_sn, csx_fwd_bind_dx, conj/ qed-.
 
-lemma csx_fwd_flat: ∀h,o,I,G,L,V,T. ⦃G, L⦄ ⊢ ⬈[h, o] 𝐒⦃ⓕ{I}V.T⦄ →
-                    ⦃G, L⦄ ⊢ ⬈[h, o] 𝐒⦃V⦄ ∧ ⦃G, L⦄ ⊢ ⬈[h, o] 𝐒⦃T⦄.
+lemma csx_fwd_flat: ∀h,o,I,G,L,V,T. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃ⓕ{I}V.T⦄ →
+                    ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃V⦄ ∧ ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T⦄.
 /3 width=3 by csx_fwd_pair_sn, csx_fwd_flat_dx, conj/ qed-.
 
 (* Basic_1: removed theorems 14:
@@ -110,3 +110,7 @@ lemma csx_fwd_flat: ∀h,o,I,G,L,V,T. ⦃G, L⦄ ⊢ ⬈[h, o] 𝐒⦃ⓕ{I}V.T
             sn3_appl_cast sn3_appl_beta sn3_appl_lref sn3_appl_abbr
             sn3_appl_appls sn3_bind sn3_appl_bind sn3_appls_bind
 *)
+(* Basic_2A1: removed theorems 6:
+              csxa_ind csxa_intro csxa_cpxs_trans csxa_intro_cpx 
+              csx_csxa csxa_csx
+*)