
We prove the following statement: If two Lagrangians L_1 and L_2 are connected by the general (invertible) substitution L_2[\phi]=L_1[f(\phi)]+(something), they result in the same Smatrix. This is not a new statement but we could not find a correct proof (or, at least, formulation) in the literature. Meanwhile, we need this theorem to give a functional formulation of the contraction procedure in effective theories. Our proof contains two parts: perturbative and functional. The former is necessary to provide a foundation for manipulations with continual integrals made in the course of the functional proof.
