lemma lprs_cpr_trans: ∀G. b_c_transitive … (cpr G) (λ_. lprs G).
/3 width=5 by b_c_trans_CTC2, lpr_cprs_trans/ qed-.

(* Basic_1: was just: pr3_pr3_pr3_t *)
(* Note: alternative proof /3 width=5 by s_r_trans_CTC1, lprs_cpr_trans/ *)
lemma lprs_cprs_trans: ∀G. b_rs_transitive … (cpr G) (λ_. lprs G).
#G @b_c_to_b_rs_trans @b_c_trans_CTC2
@b_rs_trans_TC1 /2 width=3 by lpr_cprs_trans/ (**) (* full auto too slow *)
qed-.