theorem
  0.V in A & A is linearly-closed implies A = [#]Lin(A)
proof
  assume
A1: 0.V in A & A is linearly-closed;
  thus A c= [#]Lin(A) by Th11;
  let x be object;
  assume x in [#]Lin(A);
  then x in Lin(A);
  then ex l st x = Sum(l) by MOD_3:4;
  hence thesis by A1,Th12;
end;
