proposition: Lemma Z_to_Qmult : forall x y : Z, Z_to_Q (x * y) = Qmult (Z_to_Q x) (Z_to_Q y).
proof: Proof. intros [| x| x] [| y| y]; trivial; [ apply Z_to_Qmult_POS | apply Z_to_Qmult_POS_NEG | rewrite Z.mul_comm; rewrite Qmult_sym; apply Z_to_Qmult_POS_NEG | apply Z_to_Qmult_NEG ]. Qed.
imports: Coq(FunInd) QArithSternBrocot(Field_Theory_Q)