Subtype of limited type non-limited?

[Florian Weimer <fw@deneb.cygnus.argh.org>]

The following code results in a GNAT error message:

access_discriminant.ads:21:36: access discriminants allowed 
                               only for limited types

GNAT assumes that the subtype of a limited type is non-limited (at
least under these special circumstances).  Is this really correct?

with Ada.Streams;

package Access_Discriminant is

   subtype Root_Stream_Type is Ada.Streams.Root_Stream_Type;

   type Read_Write is new Root_Stream_Type with null record;
   --  The following works:
   --  type Read_Write is new Ada.Streams.Root_Stream_Type with null record;

   procedure Read
     (Stream : in out Read_Write;
      Item   : out    Ada.Streams.Stream_Element_Array;
      Last   : out    Ada.Streams.Stream_Element_Offset);
   procedure Write
     (Stream : in out Read_Write;
      Item   : in     Ada.Streams.Stream_Element_Array);

   type Message_Sender is null record;

   type Mail_Body_Stream (Sender : access Message_Sender)
   is new Read_Write with null record;

end Access_Discriminant;