+(* EVALUATION FOR CONTEXT-SENSITIVE PARALLEL R-TRANSITION ON TERMS *********)
+
+(* Properties with context-sensitive parallel r-computation for terms ******)
+
+lemma cpre_cprs_conf (h) (G) (L) (T):
+ ∀T1. ⦃G,L⦄ ⊢ T ➡*[h] T1 → ∀T2. ⦃G,L⦄ ⊢ T ➡*[h] 𝐍⦃T2⦄ → ⦃G,L⦄ ⊢ T1 ➡*[h] 𝐍⦃T2⦄.
+#h #G #L #T0 #T1 #HT01 #T2 * #HT02 #HT2
+elim (cprs_conf … HT01 … HT02) -T0 #T0 #HT10 #HT20
+lapply (cprs_inv_cnr_sn … HT20 HT2) -HT20 #H destruct
+/2 width=1 by conj/
+qed-.