proposition: Lemma pos_ge_1 x : 0 < x ↔ 1 ≤ x.
proof: Proof. split; intros E. rewrite <-(plus_0_l 1). now apply lt_iff_plus_1_le. apply lt_le_trans with 1; [solve_propholds | easy]. Qed.
imports: Coq.setoid_ring.Ring MathClasses.interfaces.abstract_algebra MathClasses.interfaces.naturals MathClasses.interfaces.orders MathClasses.theory.naturals MathClasses.theory.rings MathClasses.implementations.peano_naturals MathClasses.orders.semirings