(** A boolean version of [le] over [nat]. See now [Nat.leb] and its properties. In scope [nat_scope], the notation for [Nat.leb] is "<=?" *)
Notation leb_iff := Nat.leb_le (only parsing).

Lemma leb_compare n m : (n <=? m) = true <-> (n ?= m) <> Gt.