(* Properties on context-sensitive parallel computation for terms ***********)
-lemma lprs_cpr_trans: ∀G. s_r_transitive … (cpr G) (λ_. lprs G).
-/3 width=5 by s_r_trans_LTC2, lpr_cprs_trans/ qed-.
+lemma lprs_cpr_trans: ∀G. c_r_transitive … (cpr G) (λ_. lprs G).
+/3 width=5 by c_r_trans_LTC2, lpr_cprs_trans/ qed-.
(* Basic_1: was just: pr3_pr3_pr3_t *)
(* Note: alternative proof /3 width=5 by s_r_trans_LTC1, lprs_cpr_trans/ *)
-lemma lprs_cprs_trans: ∀G. s_rs_transitive … (cpr G) (λ_. lprs G).
-#G @s_r_to_s_rs_trans @s_r_trans_LTC2
-@s_rs_trans_TC1 /2 width=3 by lpr_cprs_trans/ (**) (* full auto too slow *)
+lemma lprs_cprs_trans: ∀G. c_rs_transitive … (cpr G) (λ_. lprs G).
+#G @c_r_to_c_rs_trans @c_r_trans_LTC2
+@c_rs_trans_TC1 /2 width=3 by lpr_cprs_trans/ (**) (* full auto too slow *)
qed-.
lemma lprs_cprs_conf_dx: ∀G,L0,T0,T1. ⦃G, L0⦄ ⊢ T0 ➡* T1 →