In this technical note, two generalized corollaries to the LaSalle-Yoshizawa Theorem are presented for nonautonomous systems described by nonlinear differential equations with discontinuous right-hand sides. Lyapunov-based analysis methods that achieve asymptotic convergence when the candidate Lyapunov derivative is upper bounded by a negative semi-definite function in the presence of differential inclusions are presented. A design example illustrates the utility of the corollaries.