I have a region specified implicitly, and want to find the region bounds, however there are some problems when the region is defined over the integers and it is an unbounded region. This unbounded region over the reals works fine:

RegionBounds[ImplicitRegion[2 <= b <= Infinity, {b}], "Minimal"]  

{{2, \[Infinity]}}

This however, returns unevaluated:

RegionBounds[ImplicitRegion[Element[b, Integers] && 2 <= b <= Infinity, {b}], "Minimal"]

The problem is that BoundedRegionQ does not work correctly here (I suspect a bug):

BoundedRegionQ@ImplicitRegion[Element[b, Integers] && 2 <= b <= Infinity, {b}]
During evaluation of In[806]:= BoundedRegionQ::nmet: Unable to determine whether
  the region ImplicitRegion[b\[Element]Integers&&2<=b<=\[Infinity],{b}]
  is bounded. >>

Does anyone have any idea how I could overcome this issue to find the appropriate region bounds? Note, that regions can be nonconstant (containing symbolic parameters, for which ConstantBoundaryQ might return False). An example:

  ImplicitRegion[Element[(a|n), Integers] && 4 <= b <= n, {b}], 
  "Minimal"], n > 4]

where I expect the answer to be {{4, n}}, however the RegionBounds expression remains unevaluated. The correct answer is returned only if I omit the Element[(a|n), Integers] specification.

(version 10.4)


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