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

theorem
  A c= B implies Span A c= Span B
proof
  assume
A1: A c= B;
  let x be object;
  assume x in Span A;
  then ex e st x = e & e is_dependent_on A;
  then ex e st x = e & e is_dependent_on B by A1,Th29;
  hence thesis;
end;
