proposition: Lemma Zlt_cotrans_pos : forall x y : Z, (0 < x + y)%Z -> {(0 < x)%Z} + {(0 < y)%Z}.
proof: Proof. intros. case (Zlt_cotrans 0 (x + y) H x). intro. left. assumption. intro. right. apply Zplus_lt_reg_l with (p := x). rewrite Zplus_0_r. assumption. Qed.
imports: Coq(Lia)