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;
reserve e for object, X,X1,X2,Y1,Y2 for set;

theorem
  x in X \/ {y} iff x in X or x = y
proof
  x in X \/ {y} iff x in X or x in {y} by XBOOLE_0:def 3;
  hence thesis by TARSKI:def 1;
end;
