{n : ℕ} →
  {P : Sort u} →
    {parts : Multiset ℕ} →
      {parts_pos : ∀ {i : ℕ}, i ∈ parts → 0 < i} →
        {parts_sum : parts.sum = n} →
          {parts' : Multiset ℕ} →
            {parts_pos' : ∀ {i : ℕ}, i ∈ parts' → 0 < i} →
              {parts_sum' : parts'.sum = n} →
                { parts := parts, parts_pos := parts_pos, parts_sum := parts_sum } =
                    { parts := parts', parts_pos := parts_pos', parts_sum := parts_sum' } →
                  (parts = parts' → P) → P