proposition: Theorem systemunification_steps n m: 1 <= n <= m -> @SOU X n ⪯ @SOU X m.
proof: Proof. intros [H1 H2]; induction H2; eauto using systemunification_step, Nat.le_trans. Qed.
imports: PeanoNat Lia List Undecidability.HOU(calculus.calculus concon.conservativity_constants unification.higher_order_unification unification.systemunification unification.nth_order_unification)