theorem Th17:
  for X,Y be ComplexLinearSpace holds 0.
  C_VectorSpace_of_LinearOperators(X,Y) = (the carrier of X) -->0.Y
proof
  let X,Y be ComplexLinearSpace;
A1: 0.ComplexVectSpace(the carrier of X,Y) =((the carrier of X) -->0.Y) by
LOPBAN_1:def 3;
  C_VectorSpace_of_LinearOperators(X,Y) is Subspace of ComplexVectSpace(
  the carrier of X,Y) by Th13,CSSPACE:11;
  hence thesis by A1,CLVECT_1:30;
end;
