
theorem
  for M being finite-degree Matroid for A being independent Subset of M
  ex B being Basis of M st A c= B
proof
  let M be finite-degree Matroid;
  let A be independent Subset of M;
  consider B being independent Subset of M such that
A1: A c= B and
A2: B is_maximal_independent_in [#]M by Th14;
  reconsider B as Basis of M by A2,Def12;
  take B;
  thus thesis by A1;
end;
