(* Protected, structurally decreasing subtraction, and basic lemmas.  *)
(* Further properties depend on ordering conditions.                  *)

Definition subn_rec := minus.Definition subn := nosimpl subn_rec.

Lemma leq_sub m1 m2 n1 n2 : m1 <= m2 -> n2 <= n1 -> m1 - n1 <= m2 - n2.