-lemma csx_inv_lift: ∀h,o,G,L2,L1,T1,c,l,k. ⦃G, L1⦄ ⊢ ⬊*[h, o] T1 →
- ∀T2. ⬇[c, l, k] L1 ≡ L2 → ⬆[l, k] T2 ≡ T1 → ⦃G, L2⦄ ⊢ ⬊*[h, o] T2.
-#h #o #G #L2 #L1 #T1 #c #l #k #H elim H -T1 #T1 #_ #IHT1 #T2 #HL12 #HT21
+lemma csx_inv_lift: ∀h,o,G,L2,L1,T1,b,l,k. ⦃G, L1⦄ ⊢ ⬊*[h, o] T1 →
+ ∀T2. ⬇[b, l, k] L1 ≡ L2 → ⬆[l, k] T2 ≡ T1 → ⦃G, L2⦄ ⊢ ⬊*[h, o] T2.
+#h #o #G #L2 #L1 #T1 #b #l #k #H elim H -T1 #T1 #_ #IHT1 #T2 #HL12 #HT21