∀ {α : Type u_2} [inst : CommMonoid α] [inst_1 : PartialOrder α] [IsOrderedCancelMonoid α] {s : Set α} {a : α},
  (∀ i ∈ s, i < a) →
    (ThreeGPFree (insert a s) ↔ ThreeGPFree s ∧ ∀ ⦃b : α⦄, b ∈ s → ∀ ⦃c : α⦄, c ∈ s → a * c = b * b → a = b)