theorem Th28:
  Carrier(a * L) c= Carrier(L)
proof
  set T = {u : (a * L).u <> 0.GF};
  set S = {v : L.v <> 0.GF};
  T c= S
  proof
    let x be object;
    assume x in T;
    then consider u such that
A1: x = u and
A2: (a * L).u <> 0.GF;
    (a * L).u = a * L.u by Def9;
    then L.u <> 0.GF by A2;
    hence thesis by A1;
  end;
  hence thesis;
end;
