Tentative start on proving correctness

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

Utils.agda

@@ -81,3 +81,7 @@ concat-∈ : ∀ {a} {A : Set a} {x : A} {l : List A} {ls : List (List A)} →
            x ∈ l → l ∈ ls → x ∈ foldr _++_ [] ls
 concat-∈ x∈l (here refl) = ListMemProp.∈-++⁺ˡ x∈l
 concat-∈ {ls = l' ∷ ls'} x∈l (there l∈ls') = ListMemProp.∈-++⁺ʳ l' (concat-∈ x∈l l∈ls')
+
+_⇒_ : ∀ {a p₁ p₂} {A : Set a} (P : A → Set p₁) (Q : A → Set p₂) →
+      Set (a ⊔ℓ p₁ ⊔ℓ p₂)
+_⇒_ P Q = ∀ a → P a → Q a