proposition: Lemma repeat_nat_nonneg : forall n, 0 <= Core.nat_iter n (plus 1) 0.
proof: Proof. induction n;simpl. - reflexivity. - apply nonneg_plus_compat. + apply _. + apply IHn. Qed.
imports: HoTT.Classes.theory.apartness HoTT.Classes.interfaces.abstract_algebra HoTT.Classes.interfaces.orders HoTT.Classes.theory.rings HoTT.Classes.orders.orders HoTT.Classes.orders.maps