Start working on the evaluation operation.

Proving monotonicity is the main hurdle here.

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

Lattice/FiniteMap.agda

@@ -69,9 +69,15 @@ module WithKeys (ks : List A) where
                 km₁≡ks
         )
 
+    _∈_ : A × B → FiniteMap → Set (a ⊔ℓ b)
+    _∈_ k,v (m₁ , _) = k,v ∈ˡ (proj₁ m₁)
+
     _∈k_ : A → FiniteMap → Set a
     _∈k_ k (m₁ , _) = k ∈ˡ (keysᵐ m₁)
 
+    locate : ∀ {k : A} {fm : FiniteMap} → k ∈k fm → Σ B (λ v → (k , v) ∈ fm)
+    locate {k} {fm = (m , _)} k∈kfm = locateᵐ {k} {m} k∈kfm
+
     _updating_via_ : FiniteMap → List A → (A → B) → FiniteMap
     _updating_via_ (m₁ , ksm₁≡ks) ks f =
         ( m₁ updatingᵐ ks via f