
theorem
  for X,Y be RealNormSpace, L be LinearOperator of X,Y st L is onto
  holds Im(L) = the NORMSTR of Y
  proof
    let X,Y be RealNormSpace, L be LinearOperator of X,Y;
    assume L is onto; then
    the carrier of Im(L) = the carrier of Y by LCL1,IMX2;
    hence Im(L) = the NORMSTR of Y by NSUBA;
  end;
