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diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lfpxs_fqup.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lfpxs_fqup.ma
index ce2496b91..0f90e90e2 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lfpxs_fqup.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lfpxs_fqup.ma
@@ -12,31 +12,39 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/rt_transition/lfpx_fqup.ma".
+include "basic_2/i_static/tc_lfxs_fqup.ma".
 include "basic_2/rt_computation/lfpxs.ma".
 
 (* UNCOUNTED PARALLEL RT-COMPUTATION FOR LOCAL ENV.S ON REFERRED ENTRIES ****)
 
+(* Advanced properties ******************************************************)
+
+(* Basic_2A1: uses: lpxs_refl *)
+lemma lfpxs_refl: ∀h,G,T. reflexive … (lfpxs h G T).
+/2 width=1 by tc_lfxs_refl/ qed.
+
+(* Advanced forward lemmas **************************************************)
+
+lemma lfpxs_fwd_bind_dx: ∀h,p,I,G,L1,L2,V,T. ⦃G, L1⦄ ⊢ ⬈*[h, ⓑ{p,I}V.T] L2 →
+                         ⦃G, L1.ⓑ{I}V⦄ ⊢ ⬈*[h, T] L2.ⓑ{I}V.
+/2 width=2 by tc_lfxs_fwd_bind_dx/ qed-.
+
+lemma lfpxs_fwd_bind_dx_void: ∀h,p,I,G,L1,L2,V,T. ⦃G, L1⦄ ⊢ ⬈*[h, ⓑ{p,I}V.T] L2 →
+                              ⦃G, L1.ⓧ⦄ ⊢ ⬈*[h, T] L2.ⓧ.
+/2 width=4 by tc_lfxs_fwd_bind_dx_void/ qed-.
+
 (* Advanced eliminators *****************************************************)
 
-(* Basic_2A1: was just: lpxs_ind *)
-lemma lfpxs_ind: ∀h,G,L1,T. ∀R:predicate lenv. R L1 →
-                 (∀L,L2. ⦃G, L1⦄ ⊢ ⬈*[h, T] L → ⦃G, L⦄ ⊢ ⬈[h, T] L2 → R L → R L2) →
-                 ∀L2. ⦃G, L1⦄ ⊢ ⬈*[h, T] L2 → R L2.
-#h #G #L1 #T #R #HL1 #IHL1 #L2 #HL12
-@(TC_star_ind … HL1 IHL1 … HL12) //
-qed-.
+(* Basic_2A1: uses: lpxs_ind *)
+lemma lfpxs_ind_sn: ∀h,G,L1,T. ∀R:predicate lenv. R L1 →
+                    (∀L,L2. ⦃G, L1⦄ ⊢ ⬈*[h, T] L → ⦃G, L⦄ ⊢ ⬈[h, T] L2 → R L → R L2) →
+                    ∀L2. ⦃G, L1⦄ ⊢ ⬈*[h, T] L2 → R L2.
+#h #G @tc_lfxs_ind_sn // (**) (* auto fails *)
+qed-. 
 
-(* Basic_2A1: was just: lpxs_ind_dx *)
+(* Basic_2A1: uses: lpxs_ind_dx *)
 lemma lfpxs_ind_dx: ∀h,G,L2,T. ∀R:predicate lenv. R L2 →
                     (∀L1,L. ⦃G, L1⦄ ⊢ ⬈[h, T] L → ⦃G, L⦄ ⊢ ⬈*[h, T] L2 → R L → R L1) →
                     ∀L1. ⦃G, L1⦄ ⊢ ⬈*[h, T] L2 → R L1.
-#h #o #G #L2 #R #HL2 #IHL2 #L1 #HL12
-@(TC_star_ind_dx … HL2 IHL2 … HL12) //
-qed-.
-
-(* Advanced properties ******************************************************)
-
-(* Basic_2A1: was just: lpxs_refl *)
-lemma lfpxs_refl: ∀h,G,L,T. ⦃G, L⦄ ⊢ ⬈*[h, T] L.
-/2 width=1 by lfpx_lfpxs/ qed.
+#h #G @tc_lfxs_ind_dx // (**) (* auto fails *)
+qed-.