(* : nat -> nat -> Prop *)
Goal Nat.lt = lt.Notation " a =? b"  := (beq_nat a b)
                       (at level 70) : nat_scope.

(* Specifications: *)
Lemma beq_reflect : forall x y, reflect (x = y) (x =? y).
Lemma blt_reflect : forall x y, reflect (x < y) (x <? y).
Lemma ble_reflect : forall x y, reflect (x <= y) (x <=? y).