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

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

Lemma subn_if_gt T m n F (E : T) : (if m.+1 - n is m'.+1 then F m' else E) = (if n <= m then F (m - n) else E).