Rail system for the longitudinal adjustment of a vehicle seat

A rail system for the longitudinal adjustment of a vehicle seat, comprising a first rail and a second rail which are mounted on one another for longitudinal sliding along a longitudinal direction wherein each rail extends in the longitudinal direction, in the transverse direction and in the vertical direction (V), and the first rail is designed in the manner of a U-rail with two side walls and a transverse wall connecting them, and the transverse wall forms an upper side of the first rail, wherein an adjustment mechanism for the longitudinal adjustment is arranged between the two rails, and the first rail has a recess, in the region of which a transmission of the adjustment mechanism is arranged, the transmission being arranged between two retaining plates which are offset to one another in the longitudinal direction and are fastened to the first rail, which extend in the transverse direction and in the vertical direction, wherein at least one reinforcing plate extending in the transverse direction is firmly connected to the first rail on an underside opposite the upper side in the region of the recess.