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

theorem
  Span Span A = Span A
proof
  thus Span Span A c= Span A
  proof
    let x be object;
    assume x in Span Span A;
    then consider e being Element of M such that
A1: x = e and
A2: e is_dependent_on Span A;
    e is_dependent_on A by A2,Th34;
    hence thesis by A1;
  end;
  thus thesis by Th31;
end;
