
theorem
  for V being strict RealUnitarySpace,A being Subset of V holds A = the
  carrier of V implies Lin(A) = V
proof
  let V be strict RealUnitarySpace, A be Subset of V;
  assume A = the carrier of V;
  then A = the carrier of (Omega).V by RUSUB_1:def 3;
  hence Lin(A) = (Omega).V by Th5
    .= V by RUSUB_1:def 3;
end;
