reserve x,x1,x2,x3,x4,y,y1,y2,y3,y4,z,z1,z2,z2,z4 for object;

theorem
 [x1,x2,x3,x4] = [y1,y2,y3,y4]
   implies x1 = y1 & x2 = y2 & x3 = y3 & x4 = y4
proof
  assume
A1: [x1,x2,x3,x4] = [y1,y2,y3,y4];
  then [x1,x2,x3] = [y1,y2,y3] by Th1;
  hence thesis by A1,Th3,Th1;
end;
