proposition: Lemma pos_ge_1 x : 0 < x <-> 1 ≤ x.
proof: Proof. split; intros E. - rewrite <-(plus_0_l 1). apply lt_iff_plus_1_le. trivial. - apply lt_le_trans with 1; [solve_propholds | trivial]. Qed.
imports: HoTT.Classes.interfaces.abstract_algebra HoTT.Classes.interfaces.orders HoTT.Classes.theory.naturals HoTT.Classes.theory.rings HoTT.Classes.orders.semirings