proposition: Corollary continuous_composition_2arg: forall {U X Y Z : TopologicalSpace} (f : U -> X) (g : U -> Y) (h : X -> Y -> Z), continuous f -> continuous g -> continuous_2arg h -> continuous (fun p => h (f p) (g p)).
proof: Proof. intros. apply pointwise_continuity. intros. apply continuous_composition_at_2arg. - apply continuous_2arg_func_continuous_everywhere. assumption. - apply continuous_func_continuous_everywhere. assumption. - apply continuous_func_continuous_everywhere. assumption. Qed.
imports: Coq(FunctionalExtensionality) ZornsLemma(DependentTypeChoice EnsembleProduct FiniteIntersections)