2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/207928We provide a new proof of a important theorem in the Lagrangian formalism about necessary and sufficient conditions for a second-order variational system of equations to follow from a first-order Lagrangian.9 pages, LATEX, no figures; appear in Il Nuovo Cimento BHigh Energy Physics - Theorytext