proposition: Fact der_scal f (k : R) (x v : V) : derivable f x v -> (fun h => h^-1 *: ((k \*: f \o shift x) (h *: v) - (k \*: f) x)) @ (0 : R)^' --> k *: 'D_v f x.
proof: Proof. move=> df; evar (h : R -> W); rewrite [X in X @ _](_ : _ = h) /=; last first. rewrite funeqE => r. by rewrite scalerBr !scalerA mulrC -!scalerA -!scalerBr /h. exact: cvgZr. Qed.
imports: HB(structures) mathcomp(all_ssreflect ssralg ssrnum matrix interval) mathcomp(mathcomp_extra boolp classical_sets functions) reals signed topology prodnormedzmodule normedtype landau forms