theorem
  [:X1,X2,X3,X4:] = the set of all  [x1,x2,x3,x4]
proof
  defpred P[set,set,set,set] means not contradiction;
A1: for x being Element of [:X1,X2,X3,X4:] holds x in the set of all
 [x1,x2,x3,x4]
  proof
    let x be Element of [:X1,X2,X3,X4:];
    x = [x`1_4,x`2_4,x`3_4,x`4_4];
    hence thesis;
  end;
  for X1,X2,X3,X4 holds { [x1,x2,x3,x4] : P[x1,x2,x3,x4] } is Subset of [:
  X1,X2,X3,X4:] from Fraenkel4;
  then the set of all  [x1,x2,x3,x4]  is Subset of [:X1,X2,X3,X4:];
  hence thesis by A1,SUBSET_1:28;
end;
