∀ {α : Type u_1} {β : Type u_2} [inst : Preorder α] [inst_1 : Preorder β] [inst_2 : GroupWithZero α] [inst_3 : Zero β]
  [inst_4 : MulActionWithZero α β] [PosSMulMono α β] [PosSMulReflectLE α β] {s : Set β} {a : α},
  0 < a → BddBelow (a • s) = BddBelow s