Definition Urysohns_Lemma_function : point_set X -> point_set RTop.

(* Specifications: *)
Lemma Urysohns_Lemma_function_range: forall x:point_set X, 0 <= Urysohns_Lemma_function x <= 1.
Lemma Urysohns_Lemma_function_0: forall x:point_set X, In U0 x -> Urysohns_Lemma_function x = 0.
Lemma Urysohns_Lemma_function_1: forall x:point_set X, ~ In U1 x -> Urysohns_Lemma_function x = 1.
Lemma Urysohns_Lemma_function_continuous: continuous Urysohns_Lemma_function.
Theorem UrysohnsLemma: forall X:TopologicalSpace, normal_sep X -> forall F G:Ensemble (point_set X), closed F -> closed G -> Intersection F G = Empty_set -> exists f:point_set X -> point_set RTop, continuous f /\ (forall x:point_set X, 0 <= f x <= 1) /\ (forall x:point_set X, In F x -> f x = 0) /\ (forall x:point_set X, In G x -> f x = 1).