proposition: Lemma Z_to_Q_to_Z_i : forall (q:Q), Z_to_Q_i (Q_to_Z_i q) = q.
proof: Proof. intros [|qp|qp]; trivial; simpl; rewrite positive_to_Qpositive_to_positive_i; trivial. Defined.
imports: Coq(ZArith) Coq(Lia) QArithSternBrocot(Q_field)