proposition: Lemma between_nonneg (x : R) : 0 ≤ x -> -x ≤ x.
proof: Proof. intros. transitivity 0; trivial. apply flip_nonneg_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