reserve u,v,x,x1,x2,y,y1,y2,z,p,a for object,
        A,B,X,X1,X2,X3,X4,Y,Y1,Y2,Z,N,M for set;

theorem
  X \ {x} = {} implies X = {} or X = {x}
proof
  assume X \ {x} = {};
  then X c= {x} by XBOOLE_1:37;
  hence thesis by Lm3;
end;
