theorem Th10:
  a2 in a1 + W iff a1 - a2 in W
proof
  a1 - (a1 - a2) = a1 - a1 + a2 by RLVECT_1:29
    .= 0.V + a2 by VECTSP_1:19
    .= a2 by RLVECT_1:def 4;
  hence thesis by VECTSP_4:61;
end;
