theorem Th25:
  for X,Y be ComplexNormSpace holds 0.
  C_VectorSpace_of_BoundedLinearOperators(X,Y) = (the carrier of X) --> 0.Y
proof
  let X,Y be ComplexNormSpace;
A1: 0.C_VectorSpace_of_LinearOperators(X,Y) =((the carrier of X) -->0.Y) by
Th17;
  C_VectorSpace_of_BoundedLinearOperators(X,Y) is Subspace of
  C_VectorSpace_of_LinearOperators(X,Y) by Th21,CSSPACE:11;
  hence thesis by A1,CLVECT_1:30;
end;
