Canonical subfx_eval_rmorphism := AddRMorphism subfx_eval_is_rmorphism.
Definition inj_subfx := (subfx_eval \o polyC).
Canonical inj_subfx_addidive := [additive of inj_subfx].
Canonical inj_subfx_rmorphism := [rmorphism of inj_subfx].

(* Specifications: *)
Lemma subfxE x: exists p, x = subfx_eval p.
Definition subfx_scale a x := inj_subfx a * x.