Define unique as a data type to match stdlib All and Any

Map.agda

@@ -22,11 +22,12 @@ open import Data.Empty using (⊥)
 Map : Set (a ⊔ b)
 Map = List (A × B)
 
-record ⊤' : Set (a ⊔ b) where
-
-Unique : List (A × B) → Set (a ⊔ b)
-Unique [] = ⊤'
-Unique ((k , _) ∷ xs) = All (λ (k' , _) → ¬ k ≡ k') xs × Unique xs
+data Unique : List (A × B) → Set (a ⊔ b) where
+    empty : Unique []
+    push : forall {k : A} {v : B} {xs : List (A × B)}
+        → All (λ (k' , _) → ¬ k ≡ k') xs
+        → Unique xs
+        → Unique ((k , v) ∷ xs)
 
 _∈_ : (A × B) → Map → Set (a ⊔ b)
 _∈_ p m = Data.List.Membership.Propositional._∈_ p m
@@ -55,7 +56,7 @@ merge f m₁ m₂ = foldr (insert f) m₂ m₁
 
 Map-functional : ∀ (k : A) (v v' : B) (xs : List (A × B)) → Unique ((k , v) ∷ xs) → Data.List.Membership.Propositional._∈_ (k , v') ((k , v) ∷ xs) → v ≡ v'
 Map-functional k v v' _ _ (here k,v'≡k,v) = sym (cong proj₂ k,v'≡k,v)
-Map-functional k v v' xs (k≢ , _) (there k,v'∈xs) = absurd (unique-not-in xs v' (k≢ , k,v'∈xs))
+Map-functional k v v' xs (push k≢ _) (there k,v'∈xs) = absurd (unique-not-in xs v' (k≢ , k,v'∈xs))
     where
         absurd : ∀ {a} {A : Set a} →  ⊥ → A
         absurd ()