proposition: Lemma gt_1_ge_1_mult_compat x y : 1 < x → 1 ≤ y → 1 < x * y.
proof: Proof. intros. apply lt_le_trans with x; trivial. apply ge_1_mult_le_compat_r; try easy. transitivity 1. now apply le_0_1. now apply lt_le. Qed.
imports: Coq.setoid_ring.Ring MathClasses.interfaces.abstract_algebra MathClasses.interfaces.orders MathClasses.theory.rings MathClasses.orders.orders MathClasses.orders.maps