Add another utility proof

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

Utils.agda

@@ -2,9 +2,9 @@ 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.All using (All; []; _∷_; map)
 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.Binary.PropositionalEquality using (_≡_; sym; refl)
 open import Relation.Nullary using (¬_)
 
 data Unique {c} {C : Set c} : List C → Set c where
@@ -30,3 +30,7 @@ Unique-append {c} {C} {x} {x' ∷ xs'} x∉xs (push x'≢ uxs') =
 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
+
+All-x∈xs : ∀ {a} {A : Set a} (xs : List A) → All (λ x → x ∈ xs) xs
+All-x∈xs [] = []
+All-x∈xs (x ∷ xs') = here refl ∷ map there (All-x∈xs xs')