proposition: Lemma orduni_normalise_correct n I: OU n X I <-> OU n X (orduni_normalise n I).
proof: Proof. split; intros H; [eapply @OU_reduction|eapply @OU_reduction with (I := orduni_normalise n I)]. all: trivial; cbn; eapply equiv_join. 1, 3, 6, 8: rewrite eta₀_correct. all: reflexivity. Qed.
imports: List Lia Morphisms Undecidability.HOU(std.std calculus.calculus unification.higher_order_unification unification.systemunification)