proposition: Lemma ge_1_gt_1_mult_compat x y : 1 ≤ x → 1 < y → 1 < x * y.
proof: Proof. intros. rewrite commutativity. now apply gt_1_ge_1_mult_compat. Qed.
imports: Coq.setoid_ring.Ring MathClasses.interfaces.abstract_algebra MathClasses.interfaces.orders MathClasses.theory.rings MathClasses.orders.orders MathClasses.orders.maps