Clean up 'Map' to hide implementation details, extract code

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

Utils.agda

@@ -0,0 +1,32 @@
+module Utils where
+
+open import Data.List using (List; []; _∷_; _++_)
+open import Data.List.Membership.Propositional using (_∈_)
+open import Data.List.Relation.Unary.All using (All; []; _∷_)
+open import Data.List.Relation.Unary.Any using (Any; here; there) -- TODO: re-export these with nicer names from map
+open import Relation.Binary.PropositionalEquality using (_≡_; sym)
+open import Relation.Nullary using (¬_)
+
+data Unique {c} {C : Set c} : List C → Set c where
+    empty : Unique []
+    push : ∀ {x : C} {xs : List C}
+        → All (λ x' → ¬ x ≡ x') xs
+        → Unique xs
+        → Unique (x ∷ xs)
+
+Unique-append : ∀ {c} {C : Set c} {x : C} {xs : List C} →
+                ¬ 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')
+    where
+        x'≢x : ¬ x' ≡ x
+        x'≢x x'≡x = x∉xs (here (sym x'≡x))
+
+        help : {l : List C} → All (λ x'' → ¬ x' ≡ x'') l → All (λ x'' → ¬ x' ≡ x'') (l ++ (x ∷ []))
+        help {[]} _ = x'≢x ∷ []
+        help {e ∷ es} (x'≢e ∷ x'≢es) = x'≢e ∷ help x'≢es
+
+All¬-¬Any : ∀ {p c} {C : Set c} {P : C → Set p} {l : List C} → All (λ x → ¬ P x) l → ¬ Any P l
+All¬-¬Any {l = x ∷ xs} (¬Px ∷ _) (here Px) = ¬Px Px
+All¬-¬Any {l = x ∷ xs} (_ ∷ ¬Pxs) (there Pxs) = All¬-¬Any ¬Pxs Pxs