proposition: Theorem WeakConfluence_is_ChurchRosser1: R * S# <== S# * R# -> (R+S)# <== S# * R#.
proof: Proof. intro H. star_left_induction. rewrite dot_distr_left. repeat apply plus_destruct_leq. do 2 rewrite <- one_leq_star_a. rewrite dot_neutral_left. reflexivity. rewrite dot_assoc. rewrite H. rewrite <- dot_assoc. rewrite (star_trans R). reflexivity. rewrite dot_assoc. rewrite a_star_a_leq_star_a. reflexivity. Qed.
imports: ATBR(ATBR) Coq(Relations)