{α : Type u_4} →
  [inst : Semiring α] →
    [inst_1 : PartialOrder α] →
      (floor ceil : α → ℕ) →
        (∀ {a : α}, a < 0 → floor a = 0) →
          (∀ {a : α} {n : ℕ}, 0 ≤ a → (n ≤ floor a ↔ ↑n ≤ a)) → GaloisConnection ceil Nat.cast → FloorSemiring α