reserve M for finite-degree Matroid,
  A,B,C for Subset of M,
  e,f for Element of M;

theorem Th31:
  A c= Span A
proof
  let e be object;
  assume
A1: e in A;
  then reconsider x = e as Element of M;
  x is_dependent_on A by A1,Th28;
  hence thesis;
end;
