proposition: Fact dscale (f : V -> W) k x : differentiable f x -> continuous (k \*: 'd f x) /\ (k *: f) \o shift x = cst ((k *: f) x) + k \*: 'd f x +o_ (0 : V) id.
proof: Proof. move=> df; split; first by move=> ?; apply: continuousZr. apply/eqaddoE; rewrite funeqE => y /=. by rewrite -[(k *: f) _]/(_ *: _) diff_locallyx // !scalerDr scaleox. 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