proposition: Lemma preserves_le_negate1 `{!OrderPreserving f} x : x ≤ - 1 -> f x ≤ - 1.
proof: Proof. intros. rewrite <-(preserves_1 (f:=f)), <-preserves_negate. apply (order_preserving f). trivial. Qed.
imports: HoTT.Classes.interfaces.abstract_algebra HoTT.Classes.interfaces.orders HoTT.Classes.theory.groups HoTT.Classes.theory.rings HoTT.Classes.orders.semirings