Finish the last proof obligation for trace walking

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

Analysis/Forward.agda

@@ -82,7 +82,7 @@ module WithProg (prog : Program) where
     -- Finally, the map we care about is (state -> (variables -> value)). Bring that in.
     module StateVariablesFiniteMap = Lattice.FiniteValueMap.WithKeys _≟_ isLatticeᵛ states
     open StateVariablesFiniteMap
-        using (_[_]; []-∈; m₁≼m₂⇒m₁[ks]≼m₂[ks])
+        using (_[_]; []-∈; m₁≼m₂⇒m₁[ks]≼m₂[ks]; m₁≈m₂⇒k∈m₁⇒k∈km₂⇒v₁≈v₂)
         renaming
             ( FiniteMap to StateVariables
             ; isLattice to isLatticeᵐ
@@ -124,7 +124,9 @@ module WithProg (prog : Program) where
     variablesAt-∈ s sv = proj₂ (locateᵐ {s} {sv} (states-in-Map s sv))
 
     variablesAt-≈ : ∀ s sv₁ sv₂ → sv₁ ≈ᵐ sv₂ → variablesAt s sv₁ ≈ᵛ variablesAt s sv₂
-    variablesAt-≈ = {!!}
+    variablesAt-≈ s sv₁ sv₂ sv₁≈sv₂ =
+        m₁≈m₂⇒k∈m₁⇒k∈km₂⇒v₁≈v₂ sv₁ sv₂ sv₁≈sv₂
+                               (states-in-Map s sv₁) (states-in-Map s sv₂)
 
     -- build up the 'join' function, which follows from Exercise 4.26's
     --