proposition: Lemma minus_resp_ap_lft : forall x y z : G, x [#] y -> z [-] x [#] z [-] y.
proof: Proof. intros x y z H. astepl ([--] (x [-] z)). 2: unfold cg_minus in |- *; Step_final ([--] [--] z[+] [--] x). astepr ([--] (y [-] z)). 2: unfold cg_minus in |- *; Step_final ([--] [--] z[+] [--] y). apply inv_resp_ap. apply minus_resp_ap_rht. auto. Qed.
imports: CoRN.tactics.CornTac CoRN.algebra.CMonoids