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diff --git a/matita/matita/contribs/lambdadelta/basic_2/reducibility/cpr_tpss.ma b/matita/matita/contribs/lambdadelta/basic_2/reducibility/cpr_tpss.ma
index e5afe8737..fc4f2b8c5 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/reducibility/cpr_tpss.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/reducibility/cpr_tpss.ma
@@ -12,7 +12,7 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/unfold/tpss_tpss.ma".
+include "basic_2/reducibility/tpr_tpss.ma".
 include "basic_2/reducibility/cpr.ma".
 
 (* CONTEXT-SENSITIVE PARALLEL REDUCTION ON TERMS ****************************)
@@ -20,11 +20,20 @@ include "basic_2/reducibility/cpr.ma".
 (* Properties on partial unfold for terms ***********************************)
 
 lemma cpr_tpss_trans: ∀L,T1,T. L ⊢ T1 ➡ T →
-                      ∀T2. L ⊢ T ▶* [O, |L|] T2 → L ⊢ T1 ➡ T2.
-#L #T1 #T * #T0 #HT10 #HT0 #T2 #HT2
+                      ∀T2,d,e. L ⊢ T ▶* [d, e] T2 → L ⊢ T1 ➡ T2.
+#L #T1 #T * #T0 #HT10 #HT0 #T2 #d #e #HT2
+lapply (tpss_weak_all … HT2) -HT2 #HT2
 lapply (tpss_trans_eq … HT0 HT2) -T /2 width=3/
 qed.
 
 lemma cpr_tps_trans: ∀L,T1,T. L ⊢ T1 ➡ T →
-                     ∀T2. L ⊢ T ▶ [O, |L|] T2 → L ⊢ T1 ➡ T2.
-/3 width=3/ qed.
+                     ∀T2,d,e. L ⊢ T ▶ [d, e] T2 → L ⊢ T1 ➡ T2.
+/3 width=5/ qed.
+
+lemma cpr_tpss_conf: ∀L,T0,T1. L ⊢ T0 ➡ T1 →
+                     ∀T2,d,e. L ⊢ T0 ▶* [d, e] T2 →
+                     ∃∃T. L ⊢ T1 ▶* [d, e] T & L ⊢ T2 ➡ T.
+#L #T0 #T1 * #U0 #HTU0 #HU0T1 #T2 #d #e #HT02
+elim (tpr_tpss_conf … HTU0 … HT02) -T0 #T0 #HT20 #HUT0
+elim (tpss_conf_eq … HU0T1 … HUT0) -U0 /3 width=5/
+qed-.