Shadow Spaces

Let \(\Gamma(X,\sim,t,I)\) be an incidence geometry. Let \(J\) be a subset of \(I\). The shadow space \(\Gamma(J)\) of \(\Gamma\) is the incidence structure whose point-set is the set of flags of type \(J\) of \(\Gamma\) and whose blocks are the \(J-shadows\) of the flags of \(\Gamma\).

ShadowSpace(D, I): IncGeom, Set -> Inc

Given an incidence geometry \(D\) and a subset \(I\) of the set of types of \(D\), return the shadow space \(D(I)\) as an incidence structure.