Clean up imports a bit

Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>

Lattice/Prod.agda

@@ -8,11 +8,11 @@ module Lattice.Prod {a} {A B : Set a}
 
 open import Data.Nat using (ℕ; _≤_; _+_; suc)
 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.Definitions
 open import Relation.Binary.PropositionalEquality using (sym; subst)
 open import Relation.Nullary using (¬_; yes; no)
+open import Equivalence
 import Chain
 
 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 {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
-        ...   | 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)) =
                 ((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)) =