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diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fsb_fpbg.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fsb_fpbg.ma
index cdea1a396..18902f2cc 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fsb_fpbg.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fsb_fpbg.ma
@@ -12,7 +12,8 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/rt_computation/fpbg_fpbs.ma".
+include "basic_2/rt_computation/fpbg_fqup.ma".
+include "basic_2/rt_computation/fpbg_feqg.ma".
 include "basic_2/rt_computation/fsb_feqg.ma".
 
 (* STRONGLY NORMALIZING CLOSURES FOR PARALLEL RST-TRANSITION ****************)
@@ -26,17 +27,25 @@ lemma fsb_fpbs_trans:
 #G1 #L1 #T1 #H1 #IH #G2 #L2 #T2 #H12
 elim (fpbs_inv_fpbg … H12) -H12
 [ -IH /2 width=9 by fsb_feqg_trans/
-| -H1 * /2 width=5 by/
+| -H1 #H elim (fpbg_inv_fpbc_fpbs … H)
+  /2 width=5 by/
 ]
 qed-.
 
+(* Properties with parallel rst-transition for closures *********************)
+
+lemma fsb_fpb_trans:
+      ∀G1,L1,T1. ≥𝐒 ❪G1,L1,T1❫ →
+      ∀G2,L2,T2. ❪G1,L1,T1❫ ≽ ❪G2,L2,T2❫ → ≥𝐒 ❪G2,L2,T2❫.
+/3 width=5 by fsb_fpbs_trans, fpb_fpbs/ qed-.
+
 (* Properties with proper parallel rst-computation for closures *************)
 
 lemma fsb_intro_fpbg:
       ∀G1,L1,T1.
       (∀G2,L2,T2. ❪G1,L1,T1❫ > ❪G2,L2,T2❫ → ≥𝐒 ❪G2,L2,T2❫) →
       ≥𝐒 ❪G1,L1,T1❫.
-/4 width=1 by fsb_intro, fpb_fpbg/ qed.
+/4 width=1 by fsb_intro, fpbc_fpbg/ qed.
 
 (* Eliminators with proper parallel rst-computation for closures ************)
 
@@ -52,7 +61,8 @@ lemma fsb_ind_fpbg_fpbs (Q:relation3 …):
 @IH1 -IH1
 [ -IH /2 width=5 by fsb_fpbs_trans/
 | -H1 #G0 #L0 #T0 #H10
-  elim (fpbs_fpbg_trans … H12 … H10) -G2 -L2 -T2
+  lapply (fpbs_fpbg_trans … H12 … H10) -G2 -L2 -T2 #H
+  elim (fpbg_inv_fpbc_fpbs … H) -H #G #L #T #H1 #H0
   /2 width=5 by/
 ]
 qed-.