reserve u,v,x,x1,x2,y,y1,y2,z,p,a for object,
        A,B,X,X1,X2,X3,X4,Y,Y1,Y2,Z,N,M for set;
reserve e for object, X,X1,X2,Y1,Y2 for set;

theorem
  [:{x1,x2},{y1,y2}:] = {[x1,y1],[x1,y2],[x2,y1],[x2,y2]}
proof
  thus [:{x1,x2},{y1,y2}:] = [:{x1}\/{x2},{y1,y2}:] by ENUMSET1:1
    .= [:{x1},{y1,y2}:] \/ [:{x2},{y1,y2}:] by Th96
    .= {[x1,y1],[x1,y2]} \/ [:{x2},{y1,y2}:] by Th29
    .= {[x1,y1],[x1,y2]} \/ {[x2,y1],[x2,y2]} by Th29
    .= {[x1,y1],[x1,y2],[x2,y1],[x2,y2]} by ENUMSET1:5;
end;
