(* Properties concerning generic relocation *********************************)
-lemma aaa_lifts: ∀G,L1,L2,T2,A,s,des. ⬇*[s, des] L2 ≡ L1 → ∀T1. ⬆*[des] T1 ≡ T2 →
+lemma aaa_lifts: ∀G,L1,L2,T2,A,s,cs. ⬇*[s, cs] L2 ≡ L1 → ∀T1. ⬆*[cs] T1 ≡ T2 →
⦃G, L1⦄ ⊢ T1 ⁝ A → ⦃G, L2⦄ ⊢ T2 ⁝ A.
-#G #L1 #L2 #T2 #A #s #des #H elim H -L1 -L2 -des
+#G #L1 #L2 #T2 #A #s #cs #H elim H -L1 -L2 -cs
[ #L #T1 #H #HT1
<(lifts_inv_nil … H) -H //
-| #L1 #L #L2 #des #l #m #_ #HL2 #IHL1 #T1 #H #HT1
+| #L1 #L #L2 #cs #l #m #_ #HL2 #IHL1 #T1 #H #HT1
elim (lifts_inv_cons … H) -H /3 width=10 by aaa_lift/
]
qed.