Canonical add_fun_additive := Additive add_fun_is_additive.
Fact sub_fun_is_additive : additive (f \- g).
Canonical sub_fun_additive := Additive sub_fun_is_additive.
End AddFun.
Section MulFun.
Variables (R : ringType) (U : zmodType).
Variables (a : R) (f : {additive U -> R}).
Fact mull_fun_is_additive : additive (a \*o f).

Lemma bij_rmorphism :
bijective f -> exists2 f' : {rmorphism S -> R}, cancel f f' & cancel f' f.