Use prelude everywhere
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@ -1,36 +1,33 @@
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module Cat.Categories.CwF where
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open import Agda.Primitive
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open import Data.Product
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open import Cat.Prelude
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open import Cat.Category
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open import Cat.Category.Functor
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open import Cat.Categories.Fam
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open Category
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open Functor
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module _ {ℓa ℓb : Level} where
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record CwF : Set (lsuc (ℓa ⊔ ℓb)) where
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-- "A category with families consists of"
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field
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-- "A base category"
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ℂ : Category ℓa ℓb
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module ℂ = Category ℂ
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-- It's objects are called contexts
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Contexts = Object ℂ
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Contexts = ℂ.Object
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-- It's arrows are called substitutions
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Substitutions = Arrow ℂ
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Substitutions = ℂ.Arrow
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field
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-- A functor T
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T : Functor (opposite ℂ) (Fam ℓa ℓb)
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-- Empty context
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[] : Terminal ℂ
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[] : ℂ.Terminal
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private
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module T = Functor T
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Type : (Γ : Object ℂ) → Set ℓa
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Type : (Γ : ℂ.Object) → Set ℓa
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Type Γ = proj₁ (proj₁ (T.omap Γ))
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module _ {Γ : Object ℂ} {A : Type Γ} where
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module _ {Γ : ℂ.Object} {A : Type Γ} where
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-- module _ {A B : Object ℂ} {γ : ℂ [ A , B ]} where
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-- k : Σ (proj₁ (omap T B) → proj₁ (omap T A))
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@ -46,7 +43,7 @@ module _ {ℓa ℓb : Level} where
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record ContextComprehension : Set (ℓa ⊔ ℓb) where
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field
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Γ&A : Object ℂ
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Γ&A : ℂ.Object
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proj1 : ℂ [ Γ&A , Γ ]
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-- proj2 : ????
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@ -1,11 +1,9 @@
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{-# OPTIONS --allow-unsolved-metas #-}
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module Cat.Categories.Free where
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open import Agda.Primitive
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open import Relation.Binary
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open import Cat.Prelude hiding (Path ; empty)
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open import Cubical hiding (Path ; empty)
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open import Data.Product
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open import Relation.Binary
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open import Cat.Category
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@ -60,7 +58,7 @@ module _ {ℓa ℓb : Level} (ℂ : Category ℓa ℓb) where
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open Univalence isIdentity
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module _ {A B : ℂ.Object} where
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arrowsAreSets : Cubical.isSet (Path ℂ.Arrow A B)
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arrowsAreSets : isSet (Path ℂ.Arrow A B)
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arrowsAreSets a b p q = {!!}
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eqv : isEquiv (A ≡ B) (A ≅ B) (Univalence.id-to-iso isIdentity A B)
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@ -1,13 +1,7 @@
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{-# OPTIONS --allow-unsolved-metas --cubical #-}
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module Cat.Categories.Fun where
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open import Agda.Primitive
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open import Data.Product
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open import Cubical
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open import Cubical.GradLemma
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open import Cubical.NType.Properties
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open import Cat.Prelude
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open import Cat.Category
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open import Cat.Category.Functor hiding (identity)
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@ -1,12 +1,8 @@
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{-# OPTIONS --cubical --allow-unsolved-metas #-}
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module Cat.Categories.Rel where
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open import Cubical
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open import Cubical.GradLemma
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open import Agda.Primitive
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open import Data.Product renaming (proj₁ to fst ; proj₂ to snd)
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open import Cat.Prelude renaming (proj₁ to fst ; proj₂ to snd)
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open import Function
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import Cubical.FromStdLib
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open import Cat.Category
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@ -74,7 +70,7 @@ module _ {A B : Set} {S : Subset (A × B)} (ab : A × B) where
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equi : (Σ[ a' ∈ A ] (a , a') ∈ Diag A × (a' , b) ∈ S)
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≃ (a , b) ∈ S
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equi = backwards Cubical.FromStdLib., isequiv
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equi = backwards , isequiv
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ident-r : (Σ[ a' ∈ A ] (a , a') ∈ Diag A × (a' , b) ∈ S)
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≡ (a , b) ∈ S
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@ -108,7 +104,7 @@ module _ {A B : Set} {S : Subset (A × B)} (ab : A × B) where
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equi : (Σ[ b' ∈ B ] (a , b') ∈ S × (b' , b) ∈ Diag B)
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≃ ab ∈ S
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equi = backwards Cubical.FromStdLib., isequiv
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equi = backwards , isequiv
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ident-l : (Σ[ b' ∈ B ] (a , b') ∈ S × (b' , b) ∈ Diag B)
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≡ ab ∈ S
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@ -146,7 +142,7 @@ module _ {A B C D : Set} {S : Subset (A × B)} {R : Subset (B × C)} {Q : Subset
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equi : (Σ[ c ∈ C ] (Σ[ b ∈ B ] (a , b) ∈ S × (b , c) ∈ R) × (c , d) ∈ Q)
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≃ (Σ[ b ∈ B ] (a , b) ∈ S × (Σ[ c ∈ C ] (b , c) ∈ R × (c , d) ∈ Q))
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equi = fwd Cubical.FromStdLib., isequiv
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equi = fwd , isequiv
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-- isAssociativec : Q + (R + S) ≡ (Q + R) + S
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is-isAssociative : (Σ[ c ∈ C ] (Σ[ b ∈ B ] (a , b) ∈ S × (b , c) ∈ R) × (c , d) ∈ Q)
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@ -7,7 +7,6 @@ import Data.Product
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open import Function using (_∘_)
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open import Cubical hiding (_≃_)
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open import Cubical.Univalence using (univalence ; con ; _≃_ ; idtoeqv ; ua)
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open import Cat.Category
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@ -20,14 +20,7 @@ The monoidal representation is exposed by default from this module.
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{-# OPTIONS --cubical --allow-unsolved-metas #-}
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module Cat.Category.Monad where
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open import Agda.Primitive
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open import Data.Product
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open import Cubical
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open import Cubical.NType.Properties using (lemPropF ; lemSig ; lemSigP)
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open import Cubical.GradLemma using (gradLemma)
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open import Cat.Prelude
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open import Cat.Category
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open import Cat.Category.Functor as F
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open import Cat.Category.NaturalTransformation
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@ -4,11 +4,7 @@ The Kleisli formulation of monads
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{-# OPTIONS --cubical --allow-unsolved-metas #-}
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open import Agda.Primitive
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open import Data.Product
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open import Cubical
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open import Cubical.NType.Properties using (lemPropF ; lemSig ; lemSigP)
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open import Cubical.GradLemma using (gradLemma)
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open import Cat.Prelude
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open import Cat.Category
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open import Cat.Category.Functor as F
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@ -4,11 +4,7 @@ Monoidal formulation of monads
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{-# OPTIONS --cubical --allow-unsolved-metas #-}
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open import Agda.Primitive
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open import Data.Product
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open import Cubical
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open import Cubical.NType.Properties using (lemPropF ; lemSig ; lemSigP)
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open import Cubical.GradLemma using (gradLemma)
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open import Cat.Prelude
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open import Cat.Category
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open import Cat.Category.Functor as F
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@ -4,14 +4,8 @@ This module provides construction 2.3 in [voe]
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{-# OPTIONS --cubical --allow-unsolved-metas --caching #-}
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module Cat.Category.Monad.Voevodsky where
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open import Agda.Primitive
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open import Data.Product
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open import Function using (_∘_ ; _$_)
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open import Cubical
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open import Cubical.NType.Properties using (lemPropF ; lemSig ; lemSigP)
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open import Cubical.GradLemma using (gradLemma)
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open import Cat.Prelude
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open import Function
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open import Cat.Category
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open import Cat.Category.Functor as F
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@ -19,15 +19,12 @@
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-- * A composition operator.
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{-# OPTIONS --allow-unsolved-metas --cubical #-}
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module Cat.Category.NaturalTransformation where
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open import Agda.Primitive
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open import Data.Product
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open import Cat.Prelude
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open import Data.Nat using (_≤_ ; z≤n ; s≤s)
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module Nat = Data.Nat
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open import Cubical
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open import Cubical.Sigma
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open import Cubical.NType.Properties
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open import Cat.Category
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open import Cat.Category.Functor hiding (identity)
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open import Cat.Wishlist
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@ -24,7 +24,7 @@ open import Cubical.NType.Properties
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( lemPropF ; lemSig ; lemSigP ; isSetIsProp
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; propPi ; propHasLevel ; setPi ; propSet)
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public
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open import Cubical.Sigma using (setSig) public
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open import Cubical.Sigma using (setSig ; sigPresSet) public
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open import Cubical.Universe using (hSet) public
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-----------------
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