+
+(* Properties on supclosure *************************************************)
+(*
+lamma fsub_cpr_trans: ∀L1,L2,T1,T2. ⦃L1, T1⦄ ⊃ ⦃L2, T2⦄ → ∀U2. L2 ⊢ T2 ➡ U2 →
+ ∃∃L,U1. ⦃L1⦄ ➡ ⦃L⦄ & L ⊢ T1 ➡ U1 & ⦃L, U1⦄ ⊃ ⦃L2, U2⦄.
+#L1 #L2 #T1 #T2 #HT12 #U2 * #T #H1 #H2
+elim (fsub_tpr_trans … HT12 … H1) -T2 #L #U #HL1 #HT1U #HUT
+elim (fsup_tpss_trans_full … HUT … H2) -T -HUT -H2 #L #U #HL1 #HT1U #HUT
+
+
+
+
+
+
+ #H elim H -L1 -L2 -T1 -T2 [1,2,3,4,5: /3 width=5/ ]
+#L1 #K1 #K2 #T1 #T2 #U1 #d #e #HLK1 #HTU1 #_ #IHT12 #U2 #HTU2
+elim (IHT12 … HTU2) -IHT12 -HTU2 #K #T #HK1 #HT1 #HK2
+elim (lift_total T d e) #U #HTU
+elim (ldrop_ltpr_trans … HLK1 … HK1) -HLK1 -HK1 #L #HL1 #HLK
+lapply (tpr_lift … HT1 … HTU1 … HTU) -HT1 -HTU1 /3 width=11/
+qed-.
+*)
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