reserve v,x,x1,x2,x3,x4,y,y1,y2,y3,y4,z,z1,z2 for object,
  X,X1,X2,X3,X4,Y,Y1,Y2,Y3,Y4,Y5,
  Z,Z1,Z2,Z3,Z4,Z5 for set;
reserve p for pair object;
reserve R for Relation;
reserve xx1 for Element of X1,
  xx2 for Element of X2,
  xx3 for Element of X3;

theorem
  [:{x1},{x2},{x3,y3}:] = { [x1,x2,x3],[x1,x2,y3] }
proof
  thus [:{x1},{x2},{x3,y3}:] = [:[:{x1},{x2}:],{x3,y3}:] by ZFMISC_1:def 3
    .= [:{[x1,x2]},{x3,y3}:] by ZFMISC_1:29
    .= { [x1,x2,x3],[x1,x2,y3] } by ZFMISC_1:30;
end;
