
theorem
  for V being strict RealUnitarySpace, A,B being Subset of V st Lin(A) =
  V & A c= B holds Lin(B) = V
proof
  let V be strict RealUnitarySpace, A,B be Subset of V;
  assume Lin(A) = V & A c= B;
  then V is Subspace of Lin(B) by Th7;
  hence thesis by RUSUB_1:20;
end;
