
theorem Th10:
  for V being RealUnitarySpace holds (0).V + (Omega).V = the
  UNITSTR of V & (Omega).V + (0).V = the UNITSTR of V
proof
  let V be RealUnitarySpace;
  thus (0).V + (Omega).V = (Omega).V by Th9
    .= the UNITSTR of V by RUSUB_1:def 3;
  hence thesis by Lm1;
end;
