proposition: Lemma ge_1_gt_1_mult_compat x y : 1 ≤ x -> 1 < y -> 1 < x * y.
proof: Proof. intros. rewrite (commutativity (f:=mult)). apply gt_1_ge_1_mult_compat;trivial. Qed.
imports: HoTT.Classes.theory.apartness HoTT.Classes.interfaces.abstract_algebra HoTT.Classes.interfaces.orders HoTT.Classes.theory.rings HoTT.Classes.orders.orders HoTT.Classes.orders.maps