proposition: Lemma Qmult_Qdiv: forall x y z t : Q, z <> Zero -> t <> Zero -> x * t = y * z -> x / z = y / t.
proof: Proof. intros x y z t Hz Ht Hxtyz; apply Qmult_reg_l with (z*t); auto; transitivity (x*t); [|transitivity (y*z); trivial]; field; trivial. Qed.