proposition: Lemma prelift_aux_0 : forall Pt i, prelift_aux 0 Pt i = Pt.
proof: Proof. induction Pt; intro i. unfold prelift_aux. case (le_gt_dec i x); auto. auto. simpl. rewrite (IHPt (S i)); trivial. simpl. rewrite (IHPt1 i); rewrite (IHPt2 i); trivial. Qed.
imports: Coq(Compare_dec Arith Lia) CoLoR(RelExtras ListExtras LogicUtil)