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;
reserve x,y for Element of [:X1,X2,X3:];
reserve x for Element of [:X1,X2,X3,X4:];
reserve A2 for Subset of X2,
  A3 for Subset of X3,
  A4 for Subset of X4;

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;
