{α : Type u_3} →
  {inst : Preorder α} →
    {P : Sort u} →
      {pred : α → α} →
        {pred_le : ∀ (a : α), pred a ≤ a} →
          {min_of_le_pred : ∀ {a : α}, a ≤ pred a → IsMin a} →
            {le_pred_of_lt : ∀ {a b : α}, a < b → a ≤ pred b} →
              {pred' : α → α} →
                {pred_le' : ∀ (a : α), pred' a ≤ a} →
                  {min_of_le_pred' : ∀ {a : α}, a ≤ pred' a → IsMin a} →
                    {le_pred_of_lt' : ∀ {a b : α}, a < b → a ≤ pred' b} →
                      { pred := pred, pred_le := pred_le, min_of_le_pred := min_of_le_pred,
                            le_pred_of_lt := le_pred_of_lt } =
                          { pred := pred', pred_le := pred_le', min_of_le_pred := min_of_le_pred',
                            le_pred_of_lt := le_pred_of_lt' } →
                        (pred ≍ pred' → P) → P