Definition tofrac := lift_embed {fraction R} (fun x : R => Ratio x 1).
Canonical tofrac_pi_morph := PiEmbed tofrac.
Notation "x %:F"  := (@tofrac x).
Implicit Types a b c : type.
Definition addf x y : dom := Ratio (\n_x * \d_y + \n_y * \d_x) (\d_x * \d_y).
Definition add := lift_op2 {fraction R} addf.

Lemma pi_add : {morph \pi : x y / addf x y >-> add x y}.
Canonical pi_add_morph := PiMorph2 pi_add.