theorem Th32:
  for x being Element of [: base_of_frechet_filter,base_of_frechet_filter :]
  holds ex n st square-uparrow n c= x
  proof
    let x be Element of [: base_of_frechet_filter,base_of_frechet_filter :];
    ex i,j st x = [:NAT \ Segm i,NAT \ Segm j:] by Th31;
    hence thesis by Th28;
  end;
