reserve a,b,c for set;

theorem
  for X,x0 being set for A being Subset of DiscrWithInfin(X,x0) st A` is
  finite holds Int A = A
proof
  let X,x0 be set;
  let A be Subset of DiscrWithInfin(X,x0);
  assume A` is finite;
  then Cl A` = A` by Th24;
  hence Int A = A`` by TOPS_1:def 1
    .= A;
end;
