reserve Q,Q1,Q2 for multLoop;
reserve x,y,z,w,u,v for Element of Q;

theorem Th24:
  [#]lp (Nucl Q) = Nucl Q
proof
  A1: 1.Q in Nucl Q by Th20;
  A2: for x,y st x in Nucl Q & y in Nucl Q holds x * y in Nucl Q
    by Th21;
  A3: for x,y st x in Nucl Q & y in Nucl Q holds x \ y in Nucl Q
    by Th22;
   for x,y st x in Nucl Q & y in Nucl Q holds x / y in Nucl Q
     by Th23;
  hence thesis by Th18,A1,A2,A3;
end;
