proposition: Lemma pos_minus_lt_compat_r x z : 0 < z <-> x - z < x.
proof: Proof. pattern x at 2;apply (transport _ (plus_0_r x)). split; intros. - apply (strictly_order_preserving _), flip_pos_negate; assumption. - apply flip_pos_negate, (strictly_order_reflecting (x+)); assumption. Qed.
imports: HoTT.Classes.interfaces.abstract_algebra HoTT.Classes.interfaces.orders HoTT.Classes.theory.groups HoTT.Classes.theory.rings HoTT.Classes.orders.semirings