(* A closed term is invariant under lifting. *)

Lemma closed_lift_invariant:
forall `{Lift T},
forall { _ : LiftZero },
forall { _ : LiftLift },
forall { _ : LiftLiftFuse },
forall k t,
closed k t ->
forall j,
j >= k ->
forall w,
lift w j t = t.