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 invf_div x y : (x / y)^-1 = y / x.