-lemma csx_applv_delta: ∀h,I,G,L,K,V1,i. ⬇*[i] L ≘ K.ⓑ{I}V1 →
- ∀V2. ⬆*[↑i] V1 ≘ V2 →
- ∀Vs. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃ⒶVs.V2⦄ → ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃ⒶVs.#i⦄.
-#h #I #G #L #K #V1 #i #HLK #V2 #HV12 #Vs elim Vs -Vs
-[ /4 width=11 by csx_inv_lifts, csx_lref_pair, drops_isuni_fwd_drop2/
+lemma csx_applv_delta_drops (h) (G) (L):
+ ∀I,K,V1,i. ⇩[i] L ≘ K.ⓑ[I]V1 →
+ ∀V2. ⇧[↑i] V1 ≘ V2 →
+ ∀Vs. ❪G,L❫ ⊢ ⬈*𝐒[h] ⒶVs.V2 → ❪G,L❫ ⊢ ⬈*𝐒[h] ⒶVs.#i.
+#h #G #L #I #K #V1 #i #HLK #V2 #HV12 #Vs elim Vs -Vs
+[ /4 width=11 by csx_inv_lifts, csx_lref_pair_drops, drops_isuni_fwd_drop2/