Ltac Ppred_tac n :=
  apply Ppred_decrease; destruct n;
  let H := fresh "H" in intro H; try (inversion H||inversion H1); congruence.Definition Pleb (x y : positive) :=
  match Pcompare x y Eq with
    | Lt => true
    | Eq => true
    | Gt => false
  end.

Lemma Pleb_Ple (x y : positive) : Pleb x y = true <-> Ple x y.