In the ordered Abelian group of reals with the integers as a distinguished subgroup, the projection of a finite intersection of generalized halfspaces is a finite intersection of generalized halfspaces. The result is uniform in the integer coefficients and moduli of the initial generalized halfspaces.
"Generalized Halfspaces in the Mixed-Integer Realm." Notre Dame J. Formal Logic 50 (1) 43 - 51, 2009. https://doi.org/10.1215/00294527-2008-026