proposition: Lemma lift_0 : forall (M: Term), lift M 0 = M.
proof: Proof. intro M. unfold lift. destruct (lift_aux 0 M 0) as [W [envW [termW typeW]]]. simpl. apply term_eq. rewrite envW. unfold liftedEnv. simpl. rewrite finalSeg_full; trivial. rewrite termW. rewrite (prelift_aux_0 (term M) 0); trivial. Qed.
imports: Coq(Compare_dec Arith Lia) CoLoR(RelExtras ListExtras LogicUtil)