Section GenericProperties.
Variables (U : lmodType R) (V : zmodType) (s : R -> V -> V) (k : unit).
Variable f : {linear U -> V | s}.

Lemma linear0 : f 0 = 0. Proof. exact: raddf0. Qed.
Lemma linearN : {morph f : x / - x}. Proof. exact: raddfN. Qed.
Lemma linearD : {morph f : x y / x + y}. Proof. exact: raddfD. Qed.
Lemma linearB : {morph f : x y / x - y}. Proof. exact: raddfB. Qed.
Lemma linearMn n : {morph f : x / x *+ n}. Proof. exact: raddfMn. Qed.
Lemma linearMNn n : {morph f : x / x *- n}. Proof. exact: raddfMNn. Qed.
Lemma linear_sum I r (P : pred I) E :
f (\sum_(i <- r | P i) E i) = \sum_(i <- r | P i) f (E i).