∀ {A : Type u_1} [inst : AddCommMonoid A] [inst_1 : PartialOrder A] [CanonicallyOrderedAdd A]
  [inst_3 : LocallyFiniteOrderBot A] [inst_4 : DecidableEq A] {n : A} {a : A × A},
  a ∈ {uv ∈ Finset.Iic n ×ˢ Finset.Iic n | uv.1 + uv.2 = n} ↔ a.1 + a.2 = n