proposition: Lemma continuous_composition_at: forall {X Y Z:TopologicalSpace} (f:Y -> Z) (g:X -> Y) (x:X), continuous_at f (g x) -> continuous_at g x -> continuous_at (fun x:X => f (g x)) x.
proof: Proof. intros. red; intros. rewrite inverse_image_composition. auto. Qed.
imports: TopologicalSpaces Neighborhoods OpenBases NeighborhoodBases Subbases