Ltac xomega := unfold Plt, Ple in *; zify; omega.Ltac xomegaContradiction := exfalso; xomega.

(* Specifications: *)
Lemma Plt_wf: well_founded Plt.
Lemma Ppred_Plt: forall x, x <> xH -> Plt (Pos.pred x) x.
Lemma Plt_wf: well_founded Plt.
Lemma Ppred_Plt: forall x, x <> xH -> Plt (Pos.pred x) x.