theorem
  for V being strict RealLinearSpace,A,B being Subset of V holds Lin(A)
  = V & A c= B implies Lin(B) = V
proof
  let V be strict RealLinearSpace,A,B be Subset of V;
  assume Lin(A) = V & A c= B;
  then V is Subspace of Lin(B) by Th20;
  hence thesis by RLSUB_1:26;
end;
