
theorem
  for M being non void finite-degree subset-closed SubsetFamilyStr for C
  being Subset of M ex A being independent Subset of M st A
  is_maximal_independent_in C
proof
  let M be non void finite-degree subset-closed SubsetFamilyStr;
  let C be Subset of M;
  {} M c= C;
  then ex A being independent Subset of M st {} M c= A & A
  is_maximal_independent_in C by Th14;
  hence thesis;
end;
