Definition axiom (R : ringType) inv := forall x : R, x != 0 -> inv x * x = 1.
Variables (R : comRingType) (inv : R -> R).
Hypotheses (mulVf : axiom inv) (inv0 : inv 0 = 0).
Fact intro_unit (x y : R) : y * x = 1 -> x != 0.
Fact inv_out : {in predC (predC1 0), inv =1 id}.

Lemma addf_div x1 y1 x2 y2 :
y1 != 0 -> y2 != 0 -> x1 / y1 + x2 / y2 = (x1 * y2 + x2 * y1) / (y1 * y2).