theorem
  [:{x1,y1},{x2},{x3,y3}:] = { [x1,x2,x3],[y1,x2,x3],[x1,x2,y3],[y1,x2,
  y3] }
proof
  thus [:{x1,y1},{x2},{x3,y3}:] = [:[:{x1,y1},{x2}:],{x3,y3}:] by
ZFMISC_1:def 3
    .= [:{[x1,x2],[y1,x2]},{x3,y3}:] by ZFMISC_1:30
    .= { [[x1,x2],x3],[[x1,x2],y3],[[y1,x2],x3],[[y1,x2],y3] } by Th17
    .= { [x1,x2,x3],[y1,x2,x3],[x1,x2,y3],[y1,x2,y3] } by ENUMSET1:62;
end;
