reserve            x for object,
               X,Y,Z for set,
         i,j,k,l,m,n for Nat,
                 r,s for Real,
                  no for Element of OrderedNAT,
                   A for Subset of [:NAT,NAT:];
reserve X,Y,X1,X2 for non empty set,
          cA1,cB1 for filter_base of X1,
          cA2,cB2 for filter_base of X2,
              cF1 for Filter of X1,
              cF2 for Filter of X2,
             cBa1 for basis of cF1,
             cBa2 for basis of cF2;

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;
