proposition: Lemma preserves_ge_negate1 `{!OrderPreserving f} x : -1 ≤ x → -1 ≤ f x.
proof: Proof. intros. rewrite <-(preserves_1 (f:=f)), <-preserves_negate. now apply (order_preserving f). Qed.
imports: Coq.setoid_ring.Ring MathClasses.interfaces.abstract_algebra MathClasses.interfaces.orders MathClasses.theory.rings MathClasses.orders.semirings