diff --git a/src/plta/Connectives.lagda b/src/plta/Connectives.lagda index 978486cf..1ab9e5a4 100644 --- a/src/plta/Connectives.lagda +++ b/src/plta/Connectives.lagda @@ -25,11 +25,11 @@ a principle known as *Propositions as Types*. import Relation.Binary.PropositionalEquality as Eq open Eq using (_≡_; refl; sym; trans; cong) open Eq.≡-Reasoning -open import plta.Isomorphism using (_≃_; ≃-sym; ≃-trans; _≲_) -open plta.Isomorphism.≃-Reasoning open import Data.Nat using (ℕ; zero; suc; _+_; _*_) open import Data.Nat.Properties.Simple using (+-suc) open import Function using (_∘_) +open import plta.Isomorphism using (_≃_; ≃-sym; ≃-trans; _≲_) +open plta.Isomorphism.≃-Reasoning \end{code} We assume [extensionality][extensionality]. diff --git a/src/plta/Decidable.lagda b/src/plta/Decidable.lagda index 13831363..ffef6298 100644 --- a/src/plta/Decidable.lagda +++ b/src/plta/Decidable.lagda @@ -497,7 +497,8 @@ on which matches; but either is equally valid. ## Decidability of All -Recall that in Chapter [Lists]({{ site.baseurl }}{% link out/plta/Lists.md %}#All) we defined a predicate `All P` that holds if a given predicate is satisfied by every element of a list. +Recall that in Chapter [Lists]({{ site.baseurl }}{% link out/plta/Lists.md %}#All) +we defined a predicate `All P` that holds if a given predicate is satisfied by every element of a list. \begin{code} data All {A : Set} (P : A → Set) : List A → Set where [] : All P [] diff --git a/src/plta/Lists.lagda b/src/plta/Lists.lagda index cdec1037..10e195aa 100644 --- a/src/plta/Lists.lagda +++ b/src/plta/Lists.lagda @@ -23,9 +23,9 @@ open import Data.Nat.Properties using (+-assoc; +-identityˡ; +-identityʳ; *-assoc; *-identityˡ; *-identityʳ) open import Relation.Nullary using (¬_) open import Data.Product using (_×_) renaming (_,_ to ⟨_,_⟩) -open import plta.Isomorphism using (_≃_) open import Function using (_∘_) open import Level using (Level) +open import plta.Isomorphism using (_≃_) \end{code} We assume [extensionality][extensionality]. diff --git a/src/plta/Negation.lagda b/src/plta/Negation.lagda index 7dcb04a8..71a2f50e 100644 --- a/src/plta/Negation.lagda +++ b/src/plta/Negation.lagda @@ -14,13 +14,13 @@ and classical logic. ## Imports \begin{code} -open import plta.Isomorphism using (_≃_; ≃-sym; ≃-trans; _≲_) open import Relation.Binary.PropositionalEquality using (_≡_; refl) open import Data.Nat using (ℕ; zero; suc) open import Data.Empty using (⊥; ⊥-elim) open import Data.Sum using (_⊎_; inj₁; inj₂) open import Data.Product using (_×_; proj₁; proj₂) renaming (_,_ to ⟨_,_⟩) open import Function using (_∘_) +open import plta.Isomorphism using (_≃_; ≃-sym; ≃-trans; _≲_) \end{code} diff --git a/src/plta/Quantifiers.lagda b/src/plta/Quantifiers.lagda index 1a44d4db..5f9ba715 100644 --- a/src/plta/Quantifiers.lagda +++ b/src/plta/Quantifiers.lagda @@ -16,14 +16,13 @@ This chapter introduces universal and existential quantification. import Relation.Binary.PropositionalEquality as Eq open Eq using (_≡_; refl; sym; trans; cong) open Eq.≡-Reasoning -open import plta.Isomorphism using (_≃_; ≃-sym; ≃-trans; _≲_) -open plta.Isomorphism.≃-Reasoning open import Data.Nat using (ℕ; zero; suc; _+_; _*_) open import Data.Nat.Properties.Simple using (+-suc) open import Relation.Nullary using (¬_) open import Function using (_∘_) open import Data.Product using (_×_; proj₁; proj₂) renaming (_,_ to ⟨_,_⟩) open import Data.Sum using (_⊎_; inj₁; inj₂) +open import plta.Isomorphism using (_≃_; ≃-sym; ≃-trans; _≲_) \end{code} We assume [extensionality][extensionality].