proposition: Lemma preserves_gt_1 `{!StrictlyOrderPreserving f} x : 1 < x → 1 < f x.
proof: Proof. intros. rewrite <-(preserves_1 (f:=f)). now apply (strictly_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