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diff --git a/matita/matita/contribs/lambda_delta/basic_2/reducibility/tpr_tpss.ma b/matita/matita/contribs/lambda_delta/basic_2/reducibility/tpr_tpss.ma
index f3ea69327..e1ead4e44 100644
--- a/matita/matita/contribs/lambda_delta/basic_2/reducibility/tpr_tpss.ma
+++ b/matita/matita/contribs/lambda_delta/basic_2/reducibility/tpr_tpss.ma
@@ -13,7 +13,7 @@
 (**************************************************************************)
 
 include "basic_2/unfold/ltpss_dx_ltpss_dx.ma".
-include "basic_2/reducibility/ltpr_ldrop.ma".
+include "basic_2/reducibility/tpr_tps.ma".
 
 (* CONTEXT-FREE PARALLEL REDUCTION ON TERMS *********************************)
 
@@ -25,16 +25,8 @@ lemma tpr_tps_ltpr: ∀T1,T2. T1 ➡ T2 →
                     ∀L2. L1 ➡ L2 →
                     ∃∃U2. U1 ➡ U2 & L2 ⊢ T2 ▶* [d, e] U2.
 #T1 #T2 #H elim H -T1 -T2
-[ #I #L1 #d #e #X #H
-  elim (tps_inv_atom1 … H) -H
-  [ #H destruct /2 width=3/
-  | * #K1 #V1 #i #Hdi #Hide #HLK1 #HVU1 #H #L2 #HL12 destruct
-    elim (ltpr_ldrop_conf … HLK1 … HL12) -L1 #X #H #HLK2
-    elim (ltpr_inv_pair1 … H) -H #K2 #V2 #_ #HV12 #H destruct
-    elim (lift_total V2 0 (i+1)) #U2 #HVU2
-    lapply (tpr_lift … HV12 … HVU1 … HVU2) -V1 #HU12
-    @ex2_1_intro [2: @HU12 | skip | /3 width=4/ ] (**) (* /4 width=6/ is too slow *)
-  ]
+[ #I #L1 #d #e #U1 #H #L2 #HL12
+  elim (ltpr_tpr_conf … H … HL12) -L1 /3 width=3/
 | #I #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #L1 #d #e #X #H #L2 #HL12
   elim (tps_inv_flat1 … H) -H #W1 #U1 #HVW1 #HTU1 #H destruct
   elim (IHV12 … HVW1 … HL12) -V1