Definition ratio_of of phant R := ratio.Local Notation "x %:F" := (tofrac x).Canonical ratio_eqType := EqType ratio ratio_EqMixin.Canonical ratio_choiceType := ChoiceType ratio ratio_ChoiceMixin.Definition ratio0 := (@mkRatio (0, 1) (oner_neq0 _)).Definition Ratio x y : {ratio R} := insubd ratio0 (x, y).Definition numden_Ratio := (numer_Ratio, denom_Ratio).

Lemma Ratio0 x : Ratio x 0 = ratio0.