∀ {G : Type w} {α : Type u} [inst : TopologicalSpace G] [inst_1 : Group G] [IsTopologicalGroup G]
  [inst_3 : TopologicalSpace α] [inst_4 : Zero α] [T1Space α] {f : G → α},
  HasCompactSupport f → Continuous f → f = 0 ∨ LocallyCompactSpace G