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 Th30:
  for X,Y be ComplexNormSpace holds (the carrier of X) --> 0.Y =
  0.C_NormSpace_of_BoundedLinearOperators(X,Y)
proof
  let X,Y be ComplexNormSpace;
  ((the carrier of X) --> 0.Y) =0.C_VectorSpace_of_BoundedLinearOperators(
  X,Y) by Th25
    .=0.C_NormSpace_of_BoundedLinearOperators(X,Y);
  hence thesis;
end;
