
theorem Th3:
  for X be RealNormSpace holds id (the carrier of X) is Lipschitzian
  LinearOperator of X,X
proof
  let X be RealNormSpace;
A1: for v,w be VECTOR of X holds
    (id (the carrier of X)).(v+w)
      =(id (the carrier of X)).v + (id (the carrier of X)).w;
A2: for v be VECTOR of X, a be Real holds
     (id (the carrier of X)).(a*v) =a*(id (the carrier of X)).(v);
  for v be VECTOR of X holds ||.id (the carrier of X).v.|| <=1* ||.v.||;
  hence thesis by A1,A2,LOPBAN_1:def 5,def 8,VECTSP_1:def 20;
end;
