theorem
  [x1,x2,x3,x4] in [: X1,X2,X3,X4 :] iff x1 in X1 & x2 in X2 & x3 in X3
  & x4 in X4
proof
A1: [x1,x2] in [:X1,X2:] iff x1 in X1 & x2 in X2 by ZFMISC_1:87;
  [:X1,X2,X3,X4:] = [:[:X1,X2:],X3,X4:] & [x1,x2,x3,x4] = [[x1,x2],x3,x4]
  by Th38;
  hence thesis by A1,Th55;
end;
