proposition: Lemma differentiable_pair (U V' W' : normedModType R) (f : U -> V') (g : U -> W') x : differentiable f x -> differentiable g x -> differentiable (fun y => (f y, g y)) x.
proof: Proof. by move=> df dg; apply/diff_locallyP; rewrite diff_pair //; apply: dpair. 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