Start working on the evaluation operation.

Proving monotonicity is the main hurdle here.

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

Utils.agda

@@ -54,6 +54,11 @@ 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')
 
+x∈xs⇒fx∈fxs : ∀ {a b} {A : Set a} {B : Set b} (f : A → B) {x : A} {xs : List A} →
+              x ∈ xs → (f x) ∈ mapˡ f xs
+x∈xs⇒fx∈fxs f (here refl) = here refl
+x∈xs⇒fx∈fxs f (there x∈xs') = there (x∈xs⇒fx∈fxs f x∈xs')
+
 iterate : ∀ {a} {A : Set a} (n : ℕ) → (f : A → A) → A → A
 iterate 0 _ a = a
 iterate (suc n) f a = f (iterate n f a)