reserve X for non empty set;
reserve Y for ComplexLinearSpace;
reserve f,g,h for Element of Funcs(X,the carrier of Y);
reserve a,b for Complex;
reserve u,v,w for VECTOR of CLSStruct(#Funcs(X,the carrier of Y), (FuncZero(X,
    Y)),FuncAdd(X,Y),FuncExtMult(X,Y)#);

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;
