-lemma csx_fwd_applv: ∀h,o,G,L,T,Vs. ⦃G, L⦄ ⊢ ⬊*[h, o] Ⓐ Vs.T →
- ⦃G, L⦄ ⊢ ⬊*[h, o] Vs ∧ ⦃G, L⦄ ⊢ ⬊*[h, o] T.
-#h #o #G #L #T #Vs elim Vs -Vs /2 width=1 by conj/
+lemma csx_fwd_applv (G) (L):
+ ∀T,Vs. ❪G,L❫ ⊢ ⬈*𝐒 ⒶVs.T →
+ ∧∧ ❪G,L❫ ⊢ ⬈*𝐒 Vs & ❪G,L❫ ⊢ ⬈*𝐒 T.
+#G #L #T #Vs elim Vs -Vs /2 width=1 by conj/