A precise finite speed result is proved for general hyperbolic systems using neither Hamilton-Jacobi Theory as in J.L. Joly, G. Métivier, J. Rauch, Hyperbolic domains of determinacy and Hamilton-Jacobi equatiions, nor the theorem of Marchaud as in Leray. The proof is shorter than both J. Leray and J.L. Joly, G. Métivier, J. Rauch, and more general than the first. It does not give the additional information about spacelike deformations proved in J.L. Joly, G. Métivier, J. Rauch.
"Precise Finite Speed with Bare Hands." Methods Appl. Anal. 12 (3) 267 - 278, September 2005.