theorem Th48:
  (L * b) * a = L * (b * a)
proof
  let v;
  thus ((L * b) * a).v = (L * b).v * a by Def10
    .= L.v * b * a by Def10
    .= L.v * (b * a) by GROUP_1:def 3
    .= (L * (b * a)).v by Def10;
end;
