theorem
  L1 + (L2 + L3) = L1 + L2 + L3
proof
  let v;
  thus (L1 + (L2 + L3)).v = L1.v + (L2 + L3).v by Th22
    .= L1.v + (L2.v + L3.v) by Th22
    .= L1.v + L2.v + L3.v by RLVECT_1:def 3
    .= (L1 + L2).v + L3.v by Th22
    .= (L1 + L2 + L3).v by Th22;
end;
