Set Warnings "-extraction-opaque-accessed,-extraction".
Set Warnings "-notation-overridden,-parsing".
(* TODO rename this file to util.v -- not only for nats *)
(* TODO do implicits for the rest of the file *)
Set Implicit Arguments.
Unset Strict Implicit.

Lemma plus_leq_compat_r n m k :
n <= k ->
n <= m + k.