diff --git a/Map.agda b/Map.agda
index 59dfc34..44493ce 100644
--- a/Map.agda
+++ b/Map.agda
@@ -29,9 +29,6 @@ data Unique {c} {C : Set c} : List C → Set c where
         → Unique xs
         → Unique (x ∷ xs)
 
-Map : Set (a ⊔ b)
-Map = Σ (List (A × B)) (λ l → Unique (keys l))
-
 Unique-append : ∀ {c} {C : Set c} {x : C} {xs : List C} → ¬ MemProp._∈_ x xs → Unique xs →  Unique (xs ++ (x ∷ []))
 Unique-append {c} {C} {x} {[]} _ _ = push [] empty
 Unique-append {c} {C} {x} {x' ∷ xs'} x∉xs (push x'≢ uxs') = push (help x'≢) (Unique-append (λ x∈xs' → x∉xs (there x∈xs')) uxs')
@@ -43,24 +40,27 @@ Unique-append {c} {C} {x} {x' ∷ xs'} x∉xs (push x'≢ uxs') = push (help x'
         help {[]} _ = x'≢x ∷ []
         help {e ∷ es} (x'≢e ∷ x'≢es) = x'≢e ∷ help x'≢es
 
-_∈_ : (A × B) → List (A × B) → Set (a ⊔ b)
-_∈_ p m = MemProp._∈_ p m
+Map : Set (a ⊔ b)
+Map = Σ (List (A × B)) (λ l → Unique (keys l))
 
-foldr : ∀ {c} {C : Set c} → (A → B → C → C) -> C -> List (A × B) -> C
-foldr f b [] = b
-foldr f b ((k , v) ∷ xs) = f k v (foldr f b xs)
+_∈_ : (A × B) → Map → Set (a ⊔ b)
+_∈_ p (kvs , _) = MemProp._∈_ p kvs
 
 absurd : ∀ {a} {A : Set a} →  ⊥ → A
 absurd ()
 
 private module ImplRelation (_≈_ : B → B → Set b) where
     subset : List (A × B) → List (A × B) → Set (a ⊔ b)
-    subset m₁ m₂ = ∀ (k : A) (v : B) → (k , v) ∈ m₁ → Σ B (λ v' → v ≈ v' × ((k , v') ∈ m₂))
+    subset m₁ m₂ = ∀ (k : A) (v : B) → MemProp._∈_ (k , v) m₁ → Σ B (λ v' → v ≈ v' × (MemProp._∈_ (k , v') m₂))
 
 private module ImplInsert (f : B → B → B) where
     _∈k_ : A → List (A × B) → Set a
     _∈k_ k m = MemProp._∈_ k (keys m)
 
+    foldr : ∀ {c} {C : Set c} → (A → B → C → C) -> C -> List (A × B) -> C
+    foldr f b [] = b
+    foldr f b ((k , v) ∷ xs) = f k v (foldr f b xs)
+
     insert : A → B → List (A × B) → List (A × B)
     insert k v [] = (k , v) ∷ []
     insert k v (x@(k' , v') ∷ xs) with ≡-dec-A k k'