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diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpx_feqg.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpx_feqg.ma
index 518ece0be..fa73e6fa3 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpx_feqg.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpx_feqg.ma
@@ -20,16 +20,22 @@ include "basic_2/rt_transition/rpx_reqg.ma".
 
 (* Properties with generic equivalence for closures *************************)
 
-(**) (* to update *)
-lemma feqg_cpx_trans (S):
+lemma feqg_cpx_trans_cpx (S):
       reflexive … S → symmetric … S →
       ∀G1,G2,L1,L2,T1,T. ❪G1,L1,T1❫ ≛[S] ❪G2,L2,T❫ →
-      ∀T2. ❪G2,L2❫ ⊢ T ⬈ T2 →
-      ∃∃T0. ❪G1,L1❫ ⊢ T1 ⬈ T0 & ❪G1,L1,T0❫ ≛[S] ❪G2,L2,T2❫.
+      ∀T2. ❪G2,L2❫ ⊢ T ⬈ T2 → ❪G1,L1❫ ⊢ T1 ⬈ T2.
 #S #H1S #H2S #G1 #G2 #L1 #L2 #T1 #T #H #T2 #HT2
 elim (feqg_inv_gen_dx … H) -H // #H #HL12 #HT1 destruct
-lapply (reqg_cpx_trans … HL12 … HT2) // #H
+@(cpx_teqg_repl_reqg … HT2)
+/2 width=7 by reqg_sym, teqg_sym, teqg_refl/
+qed-.
+
+lemma feqg_cpx_trans_feqg (S):
+      reflexive … S → symmetric … S →
+      ∀G1,G2,L1,L2,T1,T. ❪G1,L1,T1❫ ≛[S] ❪G2,L2,T❫ →
+      ∀T2. ❪G2,L2❫ ⊢ T ⬈ T2 → ❪G1,L1,T2❫ ≛[S] ❪G2,L2,T2❫.
+#S #H1S #H2S #G1 #G2 #L1 #L2 #T1 #T #H #T2 #HT2
+elim (feqg_inv_gen_dx … H) -H // #H #HL12 #_ destruct
 lapply (cpx_reqg_conf_dx … HT2 … HL12) -HT2 -HL12 // #HL12
-lapply (teqg_cpx_trans … HT1 … H) -T // #HT12
-/4 width=4 by feqg_intro_sn, teqg_refl, ex2_intro/
+/3 width=1 by feqg_intro_sn, teqg_refl/
 qed-.