Symmetry of a phenomenological Lagrangian and Adler's principle

A method is proposed for obtaining soft-pion theorems by means of a phenomenological Lagrangian that is symmetric under group $G$. It is assumed that the Lagrangian contains an arbitrary power of the particle momenta. The resulting relations go over into Adler's selfconsistency conditions if one allows only the lowest powers of the field derivatives in the Lagrangian. It is shown that the requirement of symmetry of the Lagrangian is equi- valent to Adler's principle.