  Gravitational lensing of a background source by a foreground galaxy lens
occasionally produces four images of the source. The cusp and the fold
relations impose conditions on the ratios of magnifications of these four-image
lenses. In this theoretical investigation, we explore the sensitivity of these
relations to the presence of substructure in the lens. Starting with a smooth
lens potential, we add varying amounts of substructure, while keeping the
source position fixed, and find that the fold relation is a more robust
indicator of substructure than the cusp relation for the images. This
robustness is independent of the detailed spatial distribution of the
substructure, as well as of the ellipticity of the lensing potential and the
presence of external shear.
