(* This definition of [max] is much more pleasant to work with than the one found in Coq's standard library. It can be easily unfolded, and then [omega] takes control. *)
Definition mymax m n :=
if le_gt_dec m n then n else m.
Ltac mymax :=
unfold mymax in *; dblib_by_cases; try omega.

Lemma mymax_r:
forall i j, mymax i j >= j.