proposition: Lemma preserves_le_1 `{!OrderPreserving f} x : x ≤ 1 → f x ≤ 1.
proof: Proof. intros. rewrite <-(preserves_1 (f:=f)). now apply (order_preserving f). Qed.
imports: Coq.setoid_ring.Ring MathClasses.interfaces.abstract_algebra MathClasses.interfaces.orders MathClasses.theory.rings MathClasses.orders.orders MathClasses.orders.maps