diff --git a/Pantograph/Goal.lean b/Pantograph/Goal.lean
index d0122f5..caf0267 100644
--- a/Pantograph/Goal.lean
+++ b/Pantograph/Goal.lean
@@ -185,6 +185,92 @@ protected def GoalState.getMVarEAssignment (goalState: GoalState) (mvarId: MVarI
   let (expr, _) := instantiateMVarsCore (mctx := goalState.mctx) (e := expr)
   return expr
 
+/-- Given states `dst`, `src`, and `src'`, where `dst` and `src'` are
+descendants of `src`, replay the differential `src' - src` in `dst`. Colliding
+metavariable and lemma names will be automatically renamed to ensure there is no
+collision. This implements branch unification. Unification might be impossible
+if conflicting assignments exist. -/
+@[export pantograph_goal_state_replay]
+protected def GoalState.replay (dst : GoalState) (src src' : GoalState) : CoreM (Option GoalState) := do
+  let srcNGen := src.coreState.ngen
+  let srcNGen' := src'.coreState.ngen
+  assert! srcNGen.namePrefix == srcNGen'.namePrefix
+  assert! srcNGen.namePrefix == dst.coreState.ngen.namePrefix
+  assert! src.mctx.depth == src'.mctx.depth
+  assert! src.mctx.depth == dst.mctx.depth
+
+  let diffNGenIdx := dst.coreState.ngen.idx - srcNGen.idx
+  --let diffMVarIds := src'.mctx.decls.map λ decl => decl.index ≥ src.mctx.mvarCounter
+  let mapId : Name → Name
+    | id@(.num pref n) =>
+      if pref == srcNGen.namePrefix ∧ n ≥ srcNGen.idx then
+        .num pref (n + diffNGenIdx)
+      else
+        id
+    | id => id
+  let mapExpr (e : Expr) : CoreM Expr := Core.transform e λ
+    | .mvar { name } => pure $ .done $ .mvar ⟨mapId name⟩
+    | _ => pure .continue
+  let rec mapLevel : Level → Level
+    | .succ x => .succ (mapLevel x)
+    | .max l1 l2 => .max (mapLevel l1) (mapLevel l2)
+    | .imax l1 l2 => .imax (mapLevel l1) (mapLevel l2)
+    | .mvar { name } => .mvar ⟨mapId name⟩
+    | l => l
+  let mapLocalDecl (ldecl : LocalDecl) : CoreM LocalDecl := do
+    let ldecl := ldecl.setType (← mapExpr ldecl.type)
+    if let .some value := ldecl.value? then
+      return ldecl.setValue (← mapExpr value)
+    else
+      return ldecl
+
+  let { term := savedTerm@{ meta := savedMeta@{ core, meta := meta@{ mctx, .. } }, .. }, .. } := dst.savedState
+  let mctx := {
+    mctx with
+    mvarCounter := mctx.mvarCounter + (src'.mctx.mvarCounter - src.mctx.mvarCounter),
+    lDepth := src'.mctx.lDepth.foldl (init := mctx.lDepth) λ acc lmvarId@{ name } depth =>
+      if src.mctx.lDepth.contains lmvarId then
+        acc
+      else
+        acc.insert ⟨mapId name⟩ depth
+    decls := ← src'.mctx.decls.foldlM (init := mctx.decls) λ acc _mvarId@{ name } decl => do
+      if decl.index < src.mctx.mvarCounter then
+        return acc
+      let mvarId := ⟨mapId name⟩
+      let decl := {
+        decl with
+        lctx := ← decl.lctx.foldlM (init := .empty) λ acc decl => do
+          let decl ← mapLocalDecl decl
+          return acc.addDecl decl,
+        type := ← mapExpr decl.type,
+      }
+      return acc.insert mvarId decl
+  }
+  let ngen := {
+    core.ngen with
+    idx := core.ngen.idx + (srcNGen'.idx - srcNGen.idx)
+  }
+  return .some {
+    dst with
+    savedState := {
+      dst.savedState with
+      term := {
+        savedTerm with
+        meta := {
+          savedMeta with
+          core := {
+            core with
+            ngen,
+          }
+          meta := {
+            meta with
+            mctx,
+          }
+        }
+      },
+    },
+  }
+
 --- Tactic execution functions ---
 
 -- Mimics `Elab.Term.logUnassignedUsingErrorInfos`
diff --git a/Test/Metavar.lean b/Test/Metavar.lean
index ddd6e56..00621e6 100644
--- a/Test/Metavar.lean
+++ b/Test/Metavar.lean
@@ -260,13 +260,21 @@ def test_partial_continuation: TestM Unit := do
   -- Continuation should fail if the state does not exist:
   match state0.resume coupled_goals with
   | .error error => addTest $ LSpec.check "(continuation failure message)" (error = "Goals [_uniq.44, _uniq.45, _uniq.42, _uniq.51] are not in scope")
-  | .ok _ => addTest $ assertUnreachable "(continuation failure)"
+  | .ok _ => fail "(continuation should fail)"
   -- Continuation should fail if some goals have not been solved
   match state2.continue state1 with
   | .error error => addTest $ LSpec.check "(continuation failure message)" (error = "Target state has unresolved goals")
-  | .ok _ => addTest $ assertUnreachable "(continuation failure)"
+  | .ok _ => fail "(continuation should fail)"
   return ()
 
+def test_branch_unification : TestM Unit := do
+  let .ok expr ← elabTerm (← `(term|∀ (p q : Prop), p → p ∧ (p ∨ q))) .none | unreachable!
+  Meta.forallTelescope expr $ λ _ rootTarget => do
+    let state ← GoalState.create rootTarget
+    let .success state1 _  ← state.tacticOn 0 "exact p" | unreachable!
+    let .success state2 _  ← state.tacticOn 1 "apply Or.inl" | unreachable!
+    let state' := state2.replay state state1
+    return ()
 
 def suite (env: Environment): List (String × IO LSpec.TestSeq) :=
   let tests := [
@@ -274,7 +282,8 @@ def suite (env: Environment): List (String × IO LSpec.TestSeq) :=
     ("2 < 5", test_m_couple),
     ("2 < 5", test_m_couple_simp),
     ("Proposition Generation", test_proposition_generation),
-    ("Partial Continuation", test_partial_continuation)
+    ("Partial Continuation", test_partial_continuation),
+    ("Branch Unification", test_branch_unification),
   ]
   tests.map (fun (name, test) => (name, proofRunner env test))