In #2482, we changed that Intersection with a HalfSpace argument automatically simplifies, e.g., to HPolyhedron. While this sounded reasonable, it breaks the assumption that Intersection always results in an Intersection object. The library has at least one place where this is assumed:

Here, cap can be an HPolyhedron instead of the expected Intersection.

julia> rectify(rand(HalfSpace))
ERROR: MethodError: no method matching set_isempty!(::HPolyhedron{Float64, Vector{Float64}}, ::Bool)

Should we undo this change and rather leave this behavior to the concrete intersection operation?