theorem
  z in [: X1,X2,X3,X4 :] implies ex x1,x2,x3,x4 st x1 in X1 & x2 in X2 &
  x3 in X3 & x4 in X4 & z = [x1,x2,x3,x4]
proof
  assume z in [: X1,X2,X3,X4 :];
  then z in [:[:X1,X2,X3:],X4:] by ZFMISC_1:def 4;
  then consider x123, x4 being object such that
A1: x123 in [:X1,X2,X3:] and
A2: x4 in X4 and
A3: z = [x123,x4] by ZFMISC_1:def 2;
  consider x1, x2, x3 such that
A4: x1 in X1 & x2 in X2 & x3 in X3 and
A5: x123 = [x1,x2,x3] by A1,Th54;
  z = [x1,x2,x3,x4] by A3,A5;
  hence thesis by A2,A4;
end;
