Swich AboveBelow to using instances

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

Analysis/Sign.agda

@@ -13,6 +13,7 @@ open import Relation.Nullary using (¬_; yes; no)
 
 open import Language
 open import Lattice
+open import Equivalence
 open import Showable using (Showable; show)
 open import Utils using (_⇒_; _∧_; _∨_)
 import Analysis.Forward
@@ -44,11 +45,19 @@ _≟ᵍ_ 0ˢ + = no (λ ())
 _≟ᵍ_ 0ˢ - = no (λ ())
 _≟ᵍ_ 0ˢ 0ˢ = yes refl
 
-≡-Decidable-Sign : IsDecidable {_} {Sign} _≡_
-≡-Decidable-Sign = record { R-dec = _≟ᵍ_ }
+instance
+    ≡-equiv : IsEquivalence Sign _≡_
+    ≡-equiv = record
+        { ≈-refl = refl
+        ; ≈-sym = sym
+        ; ≈-trans = trans
+        }
+
+    ≡-Decidable-Sign : IsDecidable {_} {Sign} _≡_
+    ≡-Decidable-Sign = record { R-dec = _≟ᵍ_ }
 
 -- embelish 'sign' with a top and bottom element.
-open import Lattice.AboveBelow Sign _≡_ (record { ≈-refl = refl; ≈-sym = sym; ≈-trans = trans }) ≡-Decidable-Sign as AB
+open import Lattice.AboveBelow Sign _ as AB
     using ()
     renaming
         ( AboveBelow to SignLattice