proposition: Lemma nat_ne_0_pos x : x <> 0 <-> 0 < x.
proof: Proof. split. - destruct (nat_0_or_pos x); auto. intros E;destruct E;trivial. - intros E1 E2. rewrite E2 in E1. destruct (irreflexivity (<) 0). 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