proposition: Lemma lambda_free_normal s: lambda_free s -> normal s.
proof: Proof. induction 1; [ eauto.. |]. eapply normal_app_intro; eauto. now inv H. Qed.
imports: List Lia Arith Init.Wf Morphisms Program.Program Undecidability.HOU(concon.conservativity calculus.calculus) Undecidability.HOU.unification(systemunification nth_order_unification)