
theorem Th17:
  for M being finite-degree Matroid for C being Subset of M for A
  being independent Subset of M st A c= C holds card A <= Rnk C
proof
  let M be finite-degree Matroid;
  let C be Subset of M;
  let A be independent Subset of M;
  assume A c= C;
  then card A in {card B where B is independent Subset of M: B c= C};
  then Segm card A c= Segm Rnk C by ZFMISC_1:74;
  hence thesis by NAT_1:39;
end;
