-
-lemma cpxs_fwd_sort: ∀h,o,G,L,U,s. ⦃G, L⦄ ⊢ ⋆s ⬈*[h, o] U →
- ⋆s ≂ U ∨ ⦃G, L⦄ ⊢ ⋆(next h s) ⬈*[h, o] U.
-#h #o #G #L #U #s #H
-elim (cpxs_inv_sort1 … H) -H #n #d generalize in match s; -s @(nat_ind_plus … n) -n
-[ #s #_ #H -d destruct /2 width=1 by or_introl/
-| #n #IHn #s >plus_plus_comm_23 #Hnd #H destruct
- lapply (deg_next_SO … Hnd) -Hnd #Hnd
- elim (IHn … Hnd) -IHn
- [ #H lapply (tsts_inv_atom1 … H) -H #H >H -H /2 width=1 by or_intror/
- | generalize in match Hnd; -Hnd @(nat_ind_plus … n) -n
- /4 width=3 by cpxs_strap2, cpx_st, or_intror/
- | >iter_SO >iter_n_Sm //
- ]
+*)
+lemma cpxs_fwd_sort: ∀h,G,L,U,s. ⦃G, L⦄ ⊢ ⋆s ⬈*[h] U →
+ ⋆s ≂ U ∨ ⦃G, L⦄ ⊢ ⋆(next h s) ⬈*[h] U.
+#h #G #L #U #s #H elim (cpxs_inv_sort1 … H) -H *
+[ #H destruct /2 width=1 by or_introl/
+| #n #H destruct
+ @or_intror >iter_S <(iter_n_Sm … (next h)) // (**)