+lemma plt_step_rc: ∀p,q. p ≺ q → p < q.
+/2 width=1/
+qed.
+
+lemma plt_nil: ∀c,p. ◊ < c::p.
+/2 width=1/
+qed.
+
+lemma plt_skip: dx::◊ < ◊.
+/2 width=1/
+qed.
+
+lemma plt_comp: ∀c,p,q. p < q → c::p < c::q.
+#c #p #q #H elim H -q /3 width=1/ /3 width=3/
+qed.
+
+theorem plt_trans: transitive … plt.
+/2 width=3/
+qed-.
+
+lemma plt_refl: ∀p. p < p.
+#p elim p -p /2 width=1/
+@(plt_trans … (dx::◊)) //
+qed.
+