proposition: Lemma nat_0_or_pos x : x = 0 |_| 0 < x.
proof: Proof. destruct (trichotomy (<) 0 x) as [?|[?|?]]; auto. - left;symmetry;trivial. - destruct (nat_not_neg x). trivial. Qed.
imports: HoTT.Types.Sigma HoTT.Classes.theory.naturals HoTT.Classes.interfaces.abstract_algebra HoTT.Classes.interfaces.orders HoTT.Classes.theory.rings HoTT.Classes.orders.rings HoTT.Classes.implementations.peano_naturals HoTT.Classes.orders.nat_int