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Clean up imports a bit

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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
This commit is contained in:
Danila Fedorin 2023-09-23 16:39:11 -07:00
parent 6cd37a212f
commit 4a90a57388
2 changed files with 6 additions and 13 deletions
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13
Lattice.agda
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@ -3,20 +3,13 @@ module Lattice where
open import Equivalence open import Equivalence
import Chain import Chain
import Data.Nat.Properties as NatProps
open import Relation.Binary.PropositionalEquality as Eq using (_≡_; sym; subst)
open Eq.≡-Reasoning using (begin_; _≡⟨⟩_; step-≡; _∎)
open import Relation.Binary.Core using (_Preserves_⟶_ ) open import Relation.Binary.Core using (_Preserves_⟶_ )
open import Relation.Nullary using (Dec; ¬_; yes; no) open import Relation.Nullary using (Dec; ¬_)
open import Data.Nat as Nat using (ℕ; _≤_; _+_; suc) open import Data.Nat as Nat using (ℕ)
open import Data.Product using (_×_; Σ; _,_; proj₁; proj₂) open import Data.Product using (_×_; Σ; _,_)
open import Data.Sum using (_⊎_; inj₁; inj₂) open import Data.Sum using (_⊎_; inj₁; inj₂)
open import Agda.Primitive using (lsuc; Level) renaming (_⊔_ to _⊔ℓ_) open import Agda.Primitive using (lsuc; Level) renaming (_⊔_ to _⊔ℓ_)
open import Function.Definitions using (Injective) open import Function.Definitions using (Injective)
open import Data.Empty using (⊥)
absurd : ∀ {a} {A : Set a} → ⊥ → A
absurd ()
IsDecidable : ∀ {a} {A : Set a} (R : A → A → Set a) → Set a IsDecidable : ∀ {a} {A : Set a} (R : A → A → Set a) → Set a
IsDecidable {a} {A} R = ∀ (a₁ a₂ : A) → Dec (R a₁ a₂) IsDecidable {a} {A} R = ∀ (a₁ a₂ : A) → Dec (R a₁ a₂)

6
Lattice/Prod.agda
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@ -8,11 +8,11 @@ module Lattice.Prod {a} {A B : Set a}
open import Data.Nat using (ℕ; _≤_; _+_; suc) open import Data.Nat using (ℕ; _≤_; _+_; suc)
open import Data.Product using (_×_; Σ; _,_; proj₁; proj₂) open import Data.Product using (_×_; Σ; _,_; proj₁; proj₂)
open import Equivalence open import Data.Empty using (⊥-elim)
open import Relation.Binary.Core using (_Preserves_⟶_ ) open import Relation.Binary.Core using (_Preserves_⟶_ )
open import Relation.Binary.Definitions
open import Relation.Binary.PropositionalEquality using (sym; subst) open import Relation.Binary.PropositionalEquality using (sym; subst)
open import Relation.Nullary using (¬_; yes; no) open import Relation.Nullary using (¬_; yes; no)
open import Equivalence
import Chain import Chain
open IsLattice lA using () renaming open IsLattice lA using () renaming
@ -141,7 +141,7 @@ module _ (≈₁-dec : IsDecidable _≈₁_) (≈₂-dec : IsDecidable _≈₂_)
unzip (done (a₁≈a₂ , b₁≈b₂)) = ((0 , 0) , ((done₁ a₁≈a₂ , done₂ b₁≈b₂) , ≤-refl)) unzip (done (a₁≈a₂ , b₁≈b₂)) = ((0 , 0) , ((done₁ a₁≈a₂ , done₂ b₁≈b₂) , ≤-refl))
unzip {a₁} {a₂} {b₁} {b₂} {n} (step {(a₁ , b₁)} {(a , b)} (((d₁ , d₂) , (a₁⊔d₁≈a , b₁⊔d₂≈b)) , a₁b₁̷≈ab) (a≈a' , b≈b') a'b'a₂b₂) unzip {a₁} {a₂} {b₁} {b₂} {n} (step {(a₁ , b₁)} {(a , b)} (((d₁ , d₂) , (a₁⊔d₁≈a , b₁⊔d₂≈b)) , a₁b₁̷≈ab) (a≈a' , b≈b') a'b'a₂b₂)
with ≈₁-dec a₁ a | ≈₂-dec b₁ b | unzip a'b'a₂b₂ with ≈₁-dec a₁ a | ≈₂-dec b₁ b | unzip a'b'a₂b₂
... | yes a₁≈a | yes b₁≈b | ((n₁ , n₂) , ((c₁ , c₂) , n≤n₁+n₂)) = absurd (a₁b₁̷≈ab (a₁≈a , b₁≈b)) ... | yes a₁≈a | yes b₁≈b | ((n₁ , n₂) , ((c₁ , c₂) , n≤n₁+n₂)) = ⊥-elim (a₁b₁̷≈ab (a₁≈a , b₁≈b))
... | no a₁̷≈a | yes b₁≈b | ((n₁ , n₂) , ((c₁ , c₂) , n≤n₁+n₂)) = ... | no a₁̷≈a | yes b₁≈b | ((n₁ , n₂) , ((c₁ , c₂) , n≤n₁+n₂)) =
((suc n₁ , n₂) , ((step₁ ((d₁ , a₁⊔d₁≈a) , a₁̷≈a) a≈a' c₁ , Chain₂-≈-cong₁ (≈₂-sym (≈₂-trans b₁≈b b≈b')) c₂), +-monoʳ-≤ 1 (n≤n₁+n₂))) ((suc n₁ , n₂) , ((step₁ ((d₁ , a₁⊔d₁≈a) , a₁̷≈a) a≈a' c₁ , Chain₂-≈-cong₁ (≈₂-sym (≈₂-trans b₁≈b b≈b')) c₂), +-monoʳ-≤ 1 (n≤n₁+n₂)))
... | yes a₁≈a | no b₁̷≈b | ((n₁ , n₂) , ((c₁ , c₂) , n≤n₁+n₂)) = ... | yes a₁≈a | no b₁̷≈b | ((n₁ , n₂) , ((c₁ , c₂) , n≤n₁+n₂)) =