proposition: Lemma between_pos (x : R) : 0 < x -> -x < x.
proof: Proof. intros E. transitivity 0; trivial. apply flip_pos_negate. trivial. Qed.
imports: HoTT.Classes.interfaces.abstract_algebra HoTT.Classes.interfaces.orders HoTT.Classes.theory.groups HoTT.Classes.theory.rings HoTT.Classes.orders.semirings