Section FieldMorphismInj.
Variables (R : ringType) (f : {rmorphism F -> R}).

(* Specifications: *)
Lemma fmorph_eq0 x : (f x == 0) = (x == 0).
Lemma fmorph_inj : injective f.
Lemma fmorph_eq1 x : (f x == 1) = (x == 1).
Lemma fmorphV : {morph f: x / x^-1}.
Lemma fmorph_div : {morph f : x y / x / y}.
Lemma rpredZeq S (modS : submodPred S) (kS : keyed_pred modS) a v :
(a *: v \in kS) = (a == 0) || (v \in kS).