-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_r/
-]
-qed.
-
-lemma cpxs_bind_dx: ∀h,o,G,L,V1,V2. ⦃G, L⦄ ⊢ V1 ➡[h, o] V2 →
- ∀I,T1,T2. ⦃G, L. ⓑ{I}V1⦄ ⊢ T1 ➡*[h, o] T2 →
- ∀a. ⦃G, L⦄ ⊢ ⓑ{a,I}V1.T1 ➡*[h, o] ⓑ{a,I}V2.T2.
-#h #o #G #L #V1 #V2 #HV12 #I #T1 #T2 #HT12 #a @(cpxs_ind_dx … HT12) -T1
+lemma cpxs_bind_dx: ∀h,G,L,V1,V2. ⦃G,L⦄ ⊢ V1 ⬈[h] V2 →
+ ∀I,T1,T2. ⦃G,L. ⓑ{I}V1⦄ ⊢ T1 ⬈*[h] T2 →
+ ∀p. ⦃G,L⦄ ⊢ ⓑ{p,I}V1.T1 ⬈*[h] ⓑ{p,I}V2.T2.
+#h #G #L #V1 #V2 #HV12 #I #T1 #T2 #HT12 #a @(cpxs_ind_dx … HT12) -T1