{n m l} k : l < k -> n < m -> (k | m) -> n / k < m / k. Proof. intros lk nm km. apply gt_iff_not_leq. intro mknk. apply (@gt_iff_not_leq m n); only 1: apply nm. rewrite <- (nat_mul_div_cancel_l k m km). nrapply (leq_trans (y:=k * (n / k))). - rapply nat_mul_l_monotone. - apply nat_leq_mul_div_l. Defined.
Require Import Basics.Overture Basics.Tactics Basics.Trunc Basics.Classes