Finish the last proof obligation for trace walking

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

Lattice/Map.agda

@@ -1142,3 +1142,12 @@ m₁≼m₂⇒k∈km₁⇒k∈km₂ m₁ m₂ m₁≼m₂ k∈km₁ =
         (v' , (v≈v' , k,v'∈m₂)) = (proj₁ m₁≼m₂) _ _ k,v∈m₁m₂
     in
         forget k,v'∈m₂
+
+m₁≈m₂⇒k∈m₁⇒k∈km₂⇒v₁≈v₂ : ∀ (m₁ m₂ : Map) {k : A} →
+                         m₁ ≈ m₂ → ∀ (k∈km₁ : k ∈k m₁) (k∈km₂ : k ∈k m₂) →
+                         proj₁ (locate {m = m₁} k∈km₁) ≈₂ proj₁ (locate {m = m₂} k∈km₂)
+m₁≈m₂⇒k∈m₁⇒k∈km₂⇒v₁≈v₂ m₁ m₂ {k} (m₁⊆m₂ , m₂⊆m₁) k∈km₁ k∈km₂
+    with (v₁ , k,v₁∈m₁) ← locate {m = m₁} k∈km₁
+    with (v₂ , k,v₂∈m₂) ← locate {m = m₂} k∈km₂
+    with (v₂' , (v₁≈v₂' , k,v₂'∈m₂)) ← m₁⊆m₂ k v₁ k,v₁∈m₁
+    rewrite Map-functional {m = m₂} k,v₂∈m₂ k,v₂'∈m₂ = v₁≈v₂'