(** 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 := Nat.leb (only parsing).Notation leb_iff := Nat.leb_le (only parsing).

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