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diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lfpxs_etc.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lfpxs_etc.ma
index 0fda037b1..d8989b799 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lfpxs_etc.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lfpxs_etc.ma
@@ -1,20 +1,18 @@
 
-include "basic_2/static/lfxs_lfxs.ma".
-include "basic_2/rt_transition/lfpx_frees.ma".
-include "basic_2/rt_computation/lfpxs_fqup.ma".
+include "basic_2/static/lfxs_lex.ma".
+include "basic_2/rt_transition/cpx_etc.ma".
+include "basic_2/rt_computation/lfpxs_lpxs.ma".
 
-axiom cpx_frees_conf_lfpxs: ∀h,G,L1,T1,T2. ⦃G, L1⦄ ⊢ T1 ⬈[h] T2 →
-                            ∀f1. L1 ⊢ 𝐅*⦃T1⦄ ≡ f1 →
-                            ∀L2. ⦃G, L1⦄ ⊢ ⬈*[h, T1] L2 →
-                            ∀g1. L2 ⊢ 𝐅*⦃T1⦄ ≡ g1 →
-                            ∃∃g2. L2 ⊢ 𝐅*⦃T2⦄ ≡ g2 & g2 ⊆ g1 & g1 ⊆ f1.
+lemma R_fle_comp_LTC: ∀R. R_fle_compatible R → R_fle_compatible (LTC … R).
+#R #HR #L #T1 #T2 #H elim H -T2
+/3 width=3 by fle_trans_dx/
+qed-.
 
 lemma lfpxs_cpx_conf: ∀h,G. s_r_confluent1 … (cpx h G) (lfpxs h G).
 #h #G #L1 #T1 #T2 #HT12 #L2 #H
-lapply (cpx_frees_conf_lfpxs … HT12) -HT12 #HT12
-@(lfpxs_ind_sn … H) -L2 //
-#L #L2 #HL1 * #g1 #Hg1 #HL2 #IH
-elim (frees_total L1 T1) #f1 #Hf1
-elim (HT12 … Hf1 …  HL1 … Hg1) -T1 #g2 #Hg2 #Hg21 #_ -f1
-/4 width=7 by lfpxs_step_dx, sle_lexs_trans, ex2_intro/
+elim (tc_lfxs_inv_lex_lfeq … H) -H #L #HL1 #HL2
+lapply (lfxs_lex … HL1 T1) #H
+elim (cpx_lfxs_conf_fle … HT12 … H) -HT12 -H // #_ #HT21 #_
+@(lfpxs_lpxs_lfeq … HL1) -HL1
+@(fle_lfxs_trans … HL2) //
 qed-.