-lemma csx_applv_sort: ∀h,o,G,L,s,Vs. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃Vs⦄ → ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃ⒶVs.⋆s⦄.
-#h #o #G #L #s elim (deg_total h o s)
-#d generalize in match s; -s elim d -d
-[ /3 width=6 by csx_applv_cnx, cnx_sort, simple_atom/
-| #d #IHd #s #Hd #Vs elim Vs -Vs /2 width=1 by/
- #V #Vs #IHVs #HVVs
- elim (csxv_inv_cons … HVVs) #HV #HVs
- @csx_appl_simple_theq /2 width=1 by applv_simple, simple_atom/
- #X #H #H0
- elim (cpxs_fwd_sort_vector … o … H) -H #H
- [ elim H0 -H0 //
- | -H0 @(csx_cpxs_trans … (Ⓐ(V⨮Vs).⋆(next h s)))
- /3 width=1 by cpxs_flat_dx, deg_next_SO/
- ]
-]
-qed.
+lemma csx_applv_sort: ∀h,G,L,s,Vs. ⦃G, L⦄ ⊢ ⬈*[h] 𝐒⦃Vs⦄ → ⦃G, L⦄ ⊢ ⬈*[h] 𝐒⦃ⒶVs.⋆s⦄.
+/3 width=6 by csx_applv_cnx, cnx_sort, simple_atom/ qed.