@@ -10,15 +10,10 @@ module Relation.Nullary.Finite.Setoid where
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open import Data.Fin.Base using (Fin)
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open import Data.Nat.Base using (ℕ)
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- open import Data.Product.Base as ×
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- open import Data.Sum.Base as ⊎ using (_⊎_; inj₁; inj₂)
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- open import Data.Unit using (⊤; tt)
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- open import Function
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- open import Level renaming (suc to lsuc)
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- open import Relation.Binary using (Rel; Setoid; IsEquivalence)
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- import Relation.Binary.Reasoning.Setoid as SetR
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- import Relation.Binary.Construct.On as On
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- open import Relation.Binary.PropositionalEquality as ≡ using (_≡_)
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+ open import Function.Bundles using (Injection; Surjection; Inverse)
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+ open import Level using (Level; _⊔_) renaming (suc to lsuc)
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+ open import Relation.Binary.Bundles using (Setoid)
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+ open import Relation.Binary.PropositionalEquality.Properties using (setoid)
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private
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variable
@@ -27,17 +22,17 @@ private
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record StrictlyFinite (X : Setoid c ℓ) : Set (c ⊔ ℓ) where
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field
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size : ℕ
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- inv : Inverse X (≡. setoid (Fin size))
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+ inv : Inverse X (setoid (Fin size))
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record Subfinite (X : Setoid c ℓ) : Set (c ⊔ ℓ) where
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field
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size : ℕ
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- inj : Injection X (≡. setoid (Fin size))
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+ inj : Injection X (setoid (Fin size))
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record FinitelyEnumerable (X : Setoid c ℓ) : Set (c ⊔ ℓ) where
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field
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size : ℕ
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- srj : Surjection (≡. setoid (Fin size)) X
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+ srj : Surjection (setoid (Fin size)) X
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record InjectsIntoFinitelyEnumerable (X : Setoid c ℓ) c′ ℓ′
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: Set (c ⊔ ℓ ⊔ lsuc (c′ ⊔ ℓ′)) where
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