proposition: Lemma Q_to_Z_to_Q : forall x : Z, Q_to_Z (Z_to_Q x) = x.
proof: Proof. intros [| x| x]; trivial; unfold Z_to_Q in |- *; unfold Q_to_Z in |- *; rewrite Qpositive_to_Z_is_integer_part; reflexivity. Qed.
imports: Coq(FunInd) QArithSternBrocot(Field_Theory_Q)