proposition: Fact der_add f g (x v : V) : derivable f x v -> derivable g x v -> (fun h => h^-1 *: (((f + g) \o shift x) (h *: v) - (f + g) x)) @ 0^' --> 'D_v f x + 'D_v g x.
proof: Proof. move=> df dg. evar (fg : R -> W); rewrite [X in X @ _](_ : _ = fg) /=; last first. rewrite funeqE => h. by rewrite !scalerDr scalerN scalerDr opprD addrACA -!scalerBr /fg. exact: cvgD. 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