
theorem Th7:
  for m be non zero Element of NAT,
      f be LinearOperator of REAL-NS m,REAL-NS m
    st f is bijective
  holds
    ex g be Lipschitzian LinearOperator of REAL-NS m,REAL-NS m
    st g = f" & g is one-to-one onto
proof
  let m be non zero Element of NAT,
      f be LinearOperator of REAL-NS m,REAL-NS m;
  assume f is bijective; then

  consider g be LinearOperator of REAL-NS m,REAL-NS m
  such that
  A2: g = f" & g is one-to-one onto by REAL_NS2:85;

  REAL-NS m is finite-dimensional
  & dim(REAL-NS m) = m by REAL_NS2:62;
  then g is Lipschitzian by LOPBAN15:2;
  hence thesis by A2;
end;
