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{-# OPTIONS --guarded #-}
open import Agda.Primitive
open import Relation.Binary.PropositionalEquality using (_≡_; refl; subst; sym; trans)
open import Data.Unit using (⊤; tt)
open import Data.Nat -- using (ℕ; _+_; suc; _<_)
open import Data.Nat.Properties
open import Data.Fin using (Fin; fromℕ; fromℕ<)
open import Data.Vec using (Vec; lookup; []; _∷_; [_]; _++_; map)