Finish the last proof obligation for trace walking

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

Lattice/FiniteMap.agda

@@ -32,6 +32,7 @@ open import Lattice.Map ≡-dec-A lB as Map
         ; _[_] to _[_]ᵐ
         ; []-∈ to []ᵐ-∈
         ; m₁≼m₂⇒m₁[k]≼m₂[k] to m₁≼m₂⇒m₁[k]ᵐ≼m₂[k]ᵐ
+        ; m₁≈m₂⇒k∈m₁⇒k∈km₂⇒v₁≈v₂ to m₁≈m₂⇒k∈m₁⇒k∈km₂⇒v₁≈v₂ᵐ
         ; locate to locateᵐ
         ; keys to keysᵐ
         ; _updating_via_ to _updatingᵐ_via_
@@ -164,6 +165,11 @@ module WithKeys (ks : List A) where
                         fm₁ ≼ fm₂ → (k , v₁) ∈ fm₁ → (k , v₂) ∈ fm₂ → v₁ ≼₂ v₂
     m₁≼m₂⇒m₁[k]≼m₂[k] (m₁ , _) (m₂ , _) m₁≼m₂ k,v₁∈m₁ k,v₂∈m₂ = m₁≼m₂⇒m₁[k]ᵐ≼m₂[k]ᵐ m₁ m₂ m₁≼m₂ k,v₁∈m₁ k,v₂∈m₂
 
+    m₁≈m₂⇒k∈m₁⇒k∈km₂⇒v₁≈v₂ : ∀ (fm₁ fm₂ : FiniteMap) {k : A} →
+                             fm₁ ≈ fm₂ → ∀ (k∈kfm₁ : k ∈k fm₁) (k∈kfm₂ : k ∈k fm₂) →
+                             proj₁ (locate {fm = fm₁} k∈kfm₁) ≈₂ proj₁ (locate {fm = fm₂} k∈kfm₂)
+    m₁≈m₂⇒k∈m₁⇒k∈km₂⇒v₁≈v₂ (m₁ , _) (m₂ , _) = m₁≈m₂⇒k∈m₁⇒k∈km₂⇒v₁≈v₂ᵐ m₁ m₂
+
     module GeneralizedUpdate
              {l} {L : Set l}
              {_≈ˡ_ : L → L → Set l} {_⊔ˡ_ : L → L → L} {_⊓ˡ_ : L → L → L}