\begin{code}
import Relation.Binary.PropositionalEquality as Eq
open Eq using (_≡_; refl; cong; sym)
open Eq.≡-Reasoning using (begin_; _≡⟨⟩_; _≡⟨_⟩_; _∎)
open import Data.Nat using (ℕ; zero; suc; _+_; _*_; _∸_)
open import Data.Nat.Properties using (+-assoc)
\end{code}