theorem Th18:
  for X, Y be RealLinearSpace holds 0.
  R_VectorSpace_of_LinearOperators(X,Y) = (the carrier of X) -->0.Y
proof
  let X, Y be RealLinearSpace;
A1: 0.RealVectSpace(the carrier of X,Y) =((the carrier of X) -->0.Y);
  R_VectorSpace_of_LinearOperators(X,Y) is Subspace of RealVectSpace(the
  carrier of X,Y) by Th14,RSSPACE:11;
  hence thesis by A1,RLSUB_1:11;
end;
