{α : Type u_1} →
  {inst : Preorder α} →
    {P : Sort u} →
      {finsetIcc finsetIco finsetIoc finsetIoo : α → α → Finset α} →
        {finset_mem_Icc : ∀ (a b x : α), x ∈ finsetIcc a b ↔ a ≤ x ∧ x ≤ b} →
          {finset_mem_Ico : ∀ (a b x : α), x ∈ finsetIco a b ↔ a ≤ x ∧ x < b} →
            {finset_mem_Ioc : ∀ (a b x : α), x ∈ finsetIoc a b ↔ a < x ∧ x ≤ b} →
              {finset_mem_Ioo : ∀ (a b x : α), x ∈ finsetIoo a b ↔ a < x ∧ x < b} →
                {finsetIcc' finsetIco' finsetIoc' finsetIoo' : α → α → Finset α} →
                  {finset_mem_Icc' : ∀ (a b x : α), x ∈ finsetIcc' a b ↔ a ≤ x ∧ x ≤ b} →
                    {finset_mem_Ico' : ∀ (a b x : α), x ∈ finsetIco' a b ↔ a ≤ x ∧ x < b} →
                      {finset_mem_Ioc' : ∀ (a b x : α), x ∈ finsetIoc' a b ↔ a < x ∧ x ≤ b} →
                        {finset_mem_Ioo' : ∀ (a b x : α), x ∈ finsetIoo' a b ↔ a < x ∧ x < b} →
                          { finsetIcc := finsetIcc, finsetIco := finsetIco, finsetIoc := finsetIoc,
                                finsetIoo := finsetIoo, finset_mem_Icc := finset_mem_Icc,
                                finset_mem_Ico := finset_mem_Ico, finset_mem_Ioc := finset_mem_Ioc,
                                finset_mem_Ioo := finset_mem_Ioo } =
                              { finsetIcc := finsetIcc', finsetIco := finsetIco', finsetIoc := finsetIoc',
                                finsetIoo := finsetIoo', finset_mem_Icc := finset_mem_Icc',
                                finset_mem_Ico := finset_mem_Ico', finset_mem_Ioc := finset_mem_Ioc',
                                finset_mem_Ioo := finset_mem_Ioo' } →
                            (finsetIcc ≍ finsetIcc' →
                                finsetIco ≍ finsetIco' → finsetIoc ≍ finsetIoc' → finsetIoo ≍ finsetIoo' → P) →
                              P