
theorem Th3:
  for X be ComplexNormSpace holds id (the carrier of X) is Lipschitzian
  LinearOperator of X,X
proof
  let X be ComplexNormSpace;
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, z be Complex
   holds (id the carrier of X).(z*v) = z*(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,CLOPBAN1:def 3,def 6,VECTSP_1:def 20;
end;
