Definition mulf x y : dom := Ratio (\n_x * \n_y) (\d_x * \d_y).
Definition mul := lift_op2 {fraction R} mulf.

(* Specifications: *)
Lemma pi_mul : {morph \pi : x y / mulf x y >-> mul x y}.
Canonical pi_mul_morph := PiMorph2 pi_mul.