proposition: Lemma ord_1 A: 1 <= ord A.
proof: Proof. induction A; cbn [ord]; trivial. transitivity (S (ord A1)); eauto using Nat.max_lub_l. Qed.
imports: List Arith Lia Undecidability.HOU(std.std) Undecidability.HOU.calculus(prelim terms syntax semantics typing)