theorem
   [#]Polynom-Ring(0,R) /\ [#]Polynom-Ring (Polynom-Ring(0,R)) = {}
   proof
     set P0 = Polynom-Ring(0,R);
     assume [#]P0 /\ [#]Polynom-Ring P0 <> {}; then
     consider o be object such that
A2:  o in [#]P0 /\ [#]Polynom-Ring P0 by XBOOLE_0:def 1;
     o is Element of [#]P0 by A2,XBOOLE_0:def 4; then
     not o is Polynomial of P0 by Th22;
     hence contradiction by A2,POLYNOM3:def 10;
   end;
