(** Obsolete results about boolean comparisons over [N],
    kept for compatibility with IntMap and SMC. *)

Notation Peqb_correct := Pos.eqb_refl (only parsing).Notation Neqb_correct := N.eqb_refl (only parsing).Notation Neqb_comm := N.eqb_sym (only parsing).

(* Specifications: *)
Lemma Peqb_complete p p' : Pos.eqb p p' = true -> p = p'.
Lemma Peqb_Pcompare p p' : Pos.eqb p p' = true -> Pos.compare p p' = Eq.
Lemma Pcompare_Peqb p p' : Pos.compare p p' = Eq -> Pos.eqb p p' = true.
Lemma Neqb_Ncompare n n' : N.eqb n n' = true -> N.compare n n' = Eq.
Lemma Ncompare_Neqb n n' : N.compare n n' = Eq -> N.eqb n n' = true.
Lemma Neqb_complete n n' : N.eqb n n' = true -> n = n'.
Lemma Nxor_eq_true n n' : N.lxor n n' = 0 -> N.eqb n n' = true.