∀ {M : Type u_1} {α : Type u_2} [inst : Group M] [inst_1 : MulAction M α] {s : Set α} [Finite α],
  MulAction.IsPreprimitive ↥(fixingSubgroup M s) ↥(SubMulAction.ofFixingSubgroup M s) →
    ∀ {g : M},
      s ∪ g • s ≠ ⊤ →
        MulAction.IsPreprimitive ↥(fixingSubgroup M (s ∩ g • s)) ↥(SubMulAction.ofFixingSubgroup M (s ∩ g • s))