proposition: Lemma flip_pos_minus (x y : R) : 0 < y - x <-> x < y.
proof: Proof. pattern x at 2;apply (transport _ (plus_0_l x)). apply flip_lt_minus_r. Qed.
imports: HoTT.Classes.interfaces.abstract_algebra HoTT.Classes.interfaces.orders HoTT.Classes.theory.groups HoTT.Classes.theory.rings HoTT.Classes.orders.semirings