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;

theorem Th17:
  [:{x1,x2},{y1,y2}:] = {[x1,y1],[x1,y2],[x2,y1],[x2,y2]}
proof
  thus [:{x1,x2},{y1,y2}:] = [:{x1},{y1,y2}:] \/ [:{x2},{y1,y2}:] by
ZFMISC_1:109
    .= {[x1,y1],[x1,y2]} \/ [:{x2},{y1,y2}:] by ZFMISC_1:30
    .= {[x1,y1],[x1,y2]} \/ {[x2,y1],[x2,y2]} by ZFMISC_1:30
    .= {[x1,y1],[x1,y2],[x2,y1],[x2,y2]} by ENUMSET1:5;
end;
