proposition: Lemma diff_pair (U V' W' : normedModType R) (f : U -> V') (g : U -> W') x : differentiable f x -> differentiable g x -> 'd (fun y => (f y, g y)) x = (fun y => ('d f x y, 'd g x y)) :> (U -> V' * W').
proof: Proof. move=> df dg. pose d y := ('d f x y, 'd g x y). have lin_pair : linear d by move=> ???; rewrite /d !linearPZ. pose pairlM := GRing.isLinear.Build _ _ _ _ _ lin_pair. pose pairL : {linear _ -> _} := HB.pack d pairlM. rewrite -/d -[d]/(pairL : _ -> _). by apply: diff_unique; have [] := dpair df dg. 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