{α : Type u_2} →
  {motive : Preorder α → Sort u} →
    (t : Preorder α) →
      ([toLE : LE α] →
          [toLT : LT α] →
            (le_refl : ∀ (a : α), a ≤ a) →
              (le_trans : ∀ (a b c : α), a ≤ b → b ≤ c → a ≤ c) →
                (lt_iff_le_not_ge : ∀ (a b : α), a < b ↔ a ≤ b ∧ ¬b ≤ a) →
                  motive
                    { toLE := toLE, toLT := toLT, le_refl := le_refl, le_trans := le_trans,
                      lt_iff_le_not_ge := lt_iff_le_not_ge }) →
        motive t