-(*
-
-(* Basic_1: uses: pr3_pr2_pr2_t *)
-(* Basic_1: includes: pr3_pr0_pr2_t *)
-(* Basic_2A1: includes: lpr_cpr_trans *)
-lemma lpr_cpm_trans (n) (h) (G): s_r_transitive … (λL. cpm h G L n) (λ_. lpr h G).
-
-lemma cpr_bind2: ∀G,L,V1,V2. ⦃G, L⦄ ⊢ V1 ➡ V2 → ∀I,T1,T2. ⦃G, L.ⓑ{I}V2⦄ ⊢ T1 ➡ T2 →
- ∀a. ⦃G, L⦄ ⊢ ⓑ{a,I}V1.T1 ➡* ⓑ{a,I}V2.T2.
-/4 width=5 by lpr_cpr_trans, cprs_bind_dx, lpr_pair/ qed.
+lemma lpr_cpms_trans (n) (h) (G):
+ ∀L1,L2. ⦃G,L1⦄ ⊢ ➡[h] L2 →
+ ∀T1,T2. ⦃G,L2⦄ ⊢ T1 ➡*[n,h] T2 → ⦃G,L1⦄ ⊢ T1 ➡*[n,h] T2.
+#n #h #G #L1 #L2 #HL12 #T1 #T2 #H @(cpms_ind_sn … H) -n -T1
+/3 width=3 by lpr_cpm_trans, cpms_trans/
+qed-.