Hint Resolve Inclusion_of_Approximants.

(* Specifications: *)
Theorem Less_imp_Inclusion_of_Approximants :
Domain U D ->
forall x y : U,
In U (Carrier_of U D) x ->
In U (Carrier_of U D) y ->
Rel_of U D x y -> Included U (Approximants U D x) (Approximants U D y).
Theorem Approximants_define_element :
Domain U D ->
forall x y : U,
In U (Carrier_of U D) x ->
In U (Carrier_of U D) y -> Approximants U D x = Approximants U D y -> x = y.