Move the lattice etc. instances into Lattice.Map

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

Equivalence.agda

@@ -35,44 +35,3 @@ module IsEquivalenceInstances where
                 , IsEquivalence.≈-trans eB b₁≈b₂ b₂≈b₃
                 )
             }
-
-    module ForMap {a b} (A : Set a) (B : Set b)
-        (≡-dec-A : Decidable (_≡_ {a} {A}))
-        (_≈₂_ : B → B → Set b)
-        (eB : IsEquivalence B _≈₂_) where
-
-        open import Lattice.Map A B ≡-dec-A using (Map; lift; subset)
-        open import Data.List using (_∷_; []) -- TODO: re-export these with nicer names from map
-
-        open IsEquivalence eB renaming
-            ( ≈-refl to ≈₂-refl
-            ; ≈-sym to ≈₂-sym
-            ; ≈-trans to ≈₂-trans
-            )
-
-        _≈_ : Map → Map → Set (Agda.Primitive._⊔_ a b)
-        _≈_ = lift _≈₂_
-
-        _⊆_ : Map → Map → Set (Agda.Primitive._⊔_ a b)
-        _⊆_ = subset _≈₂_
-
-        private
-            ⊆-refl : (m : Map) →  m ⊆ m
-            ⊆-refl _ k v k,v∈m = (v , (≈₂-refl , k,v∈m))
-
-            ⊆-trans : (m₁ m₂ m₃ : Map) →  m₁ ⊆ m₂ → m₂ ⊆ m₃ → m₁ ⊆ m₃
-            ⊆-trans _ _ _ m₁⊆m₂ m₂⊆m₃ k v k,v∈m₁ =
-                let
-                    (v' , (v≈v' , k,v'∈m₂)) = m₁⊆m₂ k v k,v∈m₁
-                    (v'' , (v'≈v'' , k,v''∈m₃)) = m₂⊆m₃ k v' k,v'∈m₂
-                in (v'' , (≈₂-trans v≈v' v'≈v'' , k,v''∈m₃))
-
-        LiftEquivalence : IsEquivalence Map _≈_
-        LiftEquivalence = record
-            { ≈-refl = λ {m} → (⊆-refl m , ⊆-refl m)
-            ; ≈-sym = λ {m₁} {m₂} (m₁⊆m₂ , m₂⊆m₁) → (m₂⊆m₁ , m₁⊆m₂)
-            ; ≈-trans = λ {m₁} {m₂} {m₃} (m₁⊆m₂ , m₂⊆m₁) (m₂⊆m₃ , m₃⊆m₂) →
-                ( ⊆-trans m₁ m₂ m₃ m₁⊆m₂ m₂⊆m₃
-                , ⊆-trans m₃ m₂ m₁ m₃⊆m₂ m₂⊆m₁
-                )
-            }