reserve a,b,c,d for set,
  D,X1,X2,X3,X4 for non empty set,
  x1,y1,z1 for Element of X1,
  x2 for Element of X2,
  x3 for Element of X3,
  x4 for Element of X4,
  A1,B1 for Subset of X1;

theorem
  for x,y being Element of [:X1,X2:] st x`1=y`1 & x`2=y`2 holds x=y
proof
  let x,y be Element of [:X1,X2:];
  [x`1,x`2]=x;
  hence thesis by MCART_1:21;
end;
