(* Properties concerning generic relocation *********************************)
-lemma aaa_lifts: ∀L1,L2,T2,A,des. ⇩*[des] L2 ≡ L1 → ∀T1. ⇧*[des] T1 ≡ T2 →
- L1 ⊢ T1 ⁝ A → L2 ⊢ T2 ⁝ A.
-#L1 #L2 #T2 #A #des #H elim H -L1 -L2 -des
+lemma aaa_lifts: ∀G,L1,L2,T2,A,des. ⇩*[des] L2 ≡ L1 → ∀T1. ⇧*[des] T1 ≡ T2 →
+ ⦃G, L1⦄ ⊢ T1 ⁝ A → ⦃G, L2⦄ ⊢ T2 ⁝ A.
+#G #L1 #L2 #T2 #A #des #H elim H -L1 -L2 -des
[ #L #T1 #H #HT1
<(lifts_inv_nil … H) -H //
| #L1 #L #L2 #des #d #e #_ #HL2 #IHL1 #T1 #H #HT1