Variables (E : {subfield L}) (D : 'End(L)).
Hypothesis derD : Derivation E D.

(* Specifications: *)
Lemma Derivation1 : D 1 = 0.
Lemma Derivation_scalar x : x \in 1%VS -> D x = 0.
Lemma Derivation_horner p x :
p \is a polyOver E -> x \in E ->
D p.[x] = (map_poly D p).[x] + p^`().[x] * D x.