∀ {α : Type u_1} [inst : AddCommMonoid α] [inst_1 : PartialOrder α] [inst_2 : IsOrderedCancelAddMonoid α] {s t : Set α}
  {hs : s.IsPWO} {ht : t.IsPWO} (a : α) (motive : a ∈ {a | (Finset.addAntidiagonal hs ht a).Nonempty} → Prop)
  (x : a ∈ {a | (Finset.addAntidiagonal hs ht a).Nonempty}),
  (∀ (b : α × α) (hb : b ∈ Finset.addAntidiagonal hs ht a), motive ⋯) → motive x