
theorem LM5:
  for X be RealUnitarySpace, f be Function of X,REAL
    st f is_Lipschitzian_on the carrier of X
  holds f is_continuous_on the carrier of X
proof
  let X be RealUnitarySpace, f be Function of X,REAL;
  assume AS: f is_Lipschitzian_on the carrier of X;
  reconsider g=f as Function of RUSp2RNSp X,REAL;
  set Y=RUSp2RNSp X;
  g is_Lipschitzian_on the carrier of Y by AS,LM4; then
  g is_continuous_on the carrier of Y by NFCONT_1:46;
  hence thesis by LM3C;
end;
