proposition: Lemma convert_is_POS : forall p : positive, nat_of_P p = Zpos p :>Z.
proof: Proof. intro p. elim (p_is_some_anti_convert p). intros x H. rewrite H. rewrite nat_of_P_o_P_of_succ_nat_eq_succ. apply POS_anti_convert. Qed.
imports: Coq(Lia) CoRN.stdlib_omissions.List Coq.Logic.Eqdep_dec Coq.Setoids.Setoid