In this talk I will present two results of independent interest, the first being more mathematical in nature whereas the second more physical. I will first show that the hierarchy of so-called Higgs branch RG flows between the 6D (1,0) SCFTs known as 'A-type orbi-instantons' is given by the Hasse diagram of certain strata and transverse slices in the (conjectural) double affine Grassmannian of E8. Secondly, by leveraging the partial order naturally defined on this Hasse diagram I will present a proof of the a-theorem for 6D orbi-instanton Higgs branch RG flows, thereby exhausting the list of c-theorems in the even-dimensional (supersymmetric) setting.