 reserve o for object;
 reserve F for non almost_trivial Field;
 reserve x,a for Element of F;

theorem Th14:
   ex K being Field st [#]K /\ [#]Polynom-Ring K <> {}
   proof
     set F = the non almost_trivial Field;
     set x = the non trivial Element of F;
     reconsider o = <%0.F,1.F%> as object;
     per cases;
       suppose not o in [#]F; then
         reconsider K = ExField(x,o) as Field by Th7,Th8,Th10,Th9,Th12,Th11;
         take K;
         thus thesis by Th13;
       end;
       suppose
A1:      ex a being Element of F st a = <%0.F,1.F%>;
         take F;
         <%0.F,1.F%> in [#]Polynom-Ring F by POLYNOM3:def 10;
         hence thesis by A1,XBOOLE_0:def 4;
       end;
     end;
