-lemma lsubr_cpxs_trans: ∀h,o,G. lsub_trans … (cpxs h o G) lsubr.
-/3 width=5 by lsubr_cpx_trans, LTC_lsub_trans/
-qed-.
-
-lemma cprs_cpxs: ∀h,o,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡* T2 → ⦃G, L⦄ ⊢ T1 ➡*[h, o] T2.
-#h #o #G #L #T1 #T2 #H @(cprs_ind … H) -T2 /3 width=3 by cpxs_strap1, cpr_cpx/
-qed.
-
-lemma cpxs_sort: ∀h,o,G,L,s,d1. deg h o s d1 →
- ∀d2. d2 ≤ d1 → ⦃G, L⦄ ⊢ ⋆s ➡*[h, o] ⋆((next h)^d2 s).
-#h #o #G #L #s #d1 #Hkd1 #d2 @(nat_ind_plus … d2) -d2 /2 width=1 by cpx_cpxs/
-#d2 #IHd2 #Hd21 >iter_SO
-@(cpxs_strap1 … (⋆(iter d2 ℕ (next h) s)))
-[ /3 width=3 by lt_to_le/
-| @(cpx_st … (d1-d2-1)) <plus_minus_k_k
- /2 width=1 by deg_iter, monotonic_le_minus_c/
-]
+(* Basic_2A1: was just: cpxs_sort *)
+lemma cpxs_sort: ∀h,G,L,s,n. ⦃G, L⦄ ⊢ ⋆s ⬈*[h] ⋆((next h)^n s).
+#h #G #L #s #n elim n -n /2 width=1 by cpx_cpxs/
+#n >iter_S /2 width=3 by cpxs_strap1/