# 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.