diff --git a/src/frontends/lean/builtin_cmds.cpp b/src/frontends/lean/builtin_cmds.cpp
index 49e35cfb6..1a027ee5e 100644
--- a/src/frontends/lean/builtin_cmds.cpp
+++ b/src/frontends/lean/builtin_cmds.cpp
@@ -116,14 +116,53 @@ environment namespace_cmd(parser & p) {
     return push_scope(p.env(), p.ios(), scope_kind::Namespace, n);
 }
 
+static void redeclare_aliases(parser & p,
+                              list<pair<name, level>> old_level_entries,
+                              list<pair<name, expr>> old_entries) {
+    environment const & env = p.env();
+    if (!in_section_or_context(env))
+        return;
+    list<pair<name, expr>> new_entries = p.get_local_entries();
+    buffer<pair<name, expr>> to_redeclare;
+    name_set popped_locals;
+    while (!is_eqp(old_entries, new_entries)) {
+        pair<name, expr> entry = head(old_entries);
+        if (is_section_local_ref(entry.second))
+            to_redeclare.push_back(entry);
+        else if (is_local(entry.second))
+            popped_locals.insert(mlocal_name(entry.second));
+        old_entries = tail(old_entries);
+    }
+    name_set popped_levels;
+    list<pair<name, level>> new_level_entries = p.get_local_level_entries();
+    while (!is_eqp(old_level_entries, new_level_entries)) {
+        level const & l = head(old_level_entries).second;
+        if (is_param(l))
+            popped_levels.insert(param_id(l));
+        old_level_entries = tail(old_level_entries);
+    }
+
+    for (auto const & entry : to_redeclare) {
+        expr new_ref = update_section_local_ref(entry.second, popped_levels, popped_locals);
+        if (!is_constant(new_ref))
+            p.add_local_expr(entry.first, new_ref);
+    }
+}
+
 environment end_scoped_cmd(parser & p) {
+    list<pair<name, level>> level_entries = p.get_local_level_entries();
+    list<pair<name, expr>> entries        = p.get_local_entries();
     if (in_section_or_context(p.env()))
         p.pop_local_scope();
     if (p.curr_is_identifier()) {
         name n = p.check_atomic_id_next("invalid end of scope, atomic identifier expected");
-        return pop_scope(p.env(), n);
+        environment env = pop_scope(p.env(), n);
+        redeclare_aliases(p, level_entries, entries);
+        return env;
     } else {
-        return pop_scope(p.env());
+        environment env = pop_scope(p.env());
+        redeclare_aliases(p, level_entries, entries);
+        return env;
     }
 }
 
diff --git a/src/frontends/lean/local_decls.h b/src/frontends/lean/local_decls.h
index 56df2dea6..407370c2a 100644
--- a/src/frontends/lean/local_decls.h
+++ b/src/frontends/lean/local_decls.h
@@ -20,29 +20,30 @@ namespace lean {
 template<typename V>
 class local_decls {
     typedef name_map<pair<V, unsigned>> map;
-    typedef list<std::tuple<map, unsigned, list<V>>> scopes;
-    map       m_map;
-    unsigned  m_counter;
-    scopes    m_scopes;
-    list<V>   m_values;
+    typedef list<pair<name, V>> entries;
+    typedef std::tuple<map, unsigned, entries> scope;
+    typedef list<scope> scopes;
+    map      m_map;
+    unsigned m_counter;
+    scopes   m_scopes;
+    entries  m_entries;
 public:
     local_decls():m_counter(1) {}
-    local_decls(local_decls const & d):m_map(d.m_map), m_counter(d.m_counter), m_scopes(d.m_scopes) {}
+    local_decls(local_decls const & d):
+        m_map(d.m_map), m_counter(d.m_counter), m_scopes(d.m_scopes), m_entries(d.m_entries) {}
     void insert(name const & k, V const & v) {
         m_map.insert(k, mk_pair(v, m_counter));
         m_counter++;
-        m_values = cons(v, m_values);
+        m_entries = cons(mk_pair(k, v), m_entries);
     }
     V const * find(name const & k) const { auto it = m_map.find(k); return it ? &(it->first) : nullptr; }
     unsigned find_idx(name const & k) const { auto it = m_map.find(k); return it ? it->second : 0; }
     bool contains(name const & k) const { return m_map.contains(k); }
-    list<V> const & get_values() const { return m_values; }
-    void push() { m_scopes = scopes(std::make_tuple(m_map, m_counter, m_values), m_scopes); }
+    entries const & get_entries() const { return m_entries; }
+    void push() { m_scopes = cons(scope(m_map, m_counter, m_entries), m_scopes); }
     void pop() {
         lean_assert(!is_nil(m_scopes));
-        m_map     = std::get<0>(head(m_scopes));
-        m_counter = std::get<1>(head(m_scopes));
-        m_values  = std::get<2>(head(m_scopes));
+        std::tie(m_map, m_counter, m_entries) = head(m_scopes);
         m_scopes  = tail(m_scopes);
     }
     struct mk_scope {
diff --git a/src/frontends/lean/parser.cpp b/src/frontends/lean/parser.cpp
index c2b3275b5..6a2cff199 100644
--- a/src/frontends/lean/parser.cpp
+++ b/src/frontends/lean/parser.cpp
@@ -464,7 +464,11 @@ void parser::get_include_variables(buffer<expr> & vars) const {
 }
 
 list<expr> parser::locals_to_context() const {
-    return filter(m_local_decls.get_values(), [](expr const & e) { return is_local(e); });
+    return map_filter<expr>(m_local_decls.get_entries(),
+                            [](pair<name, expr> const & p, expr & out) {
+                                out = p.second;
+                                return is_local(p.second);
+                            });
 }
 
 static unsigned g_level_add_prec = 10;
diff --git a/src/frontends/lean/parser.h b/src/frontends/lean/parser.h
index fb9e595bd..7fbbd87e7 100644
--- a/src/frontends/lean/parser.h
+++ b/src/frontends/lean/parser.h
@@ -348,9 +348,11 @@ public:
     expr const * get_local(name const & n) const { return m_local_decls.find(n); }
     /** \brief Return local declarations as a list of local constants. */
     list<expr> locals_to_context() const;
-
-    /**
-        \brief By default, when the parser finds a unknown identifier, it signs an error.
+    /** \brief Return all local declarations and aliases */
+    list<pair<name, expr>> const & get_local_entries() const { return m_local_decls.get_entries(); }
+    /** \brief Return all local level declarations */
+    list<pair<name, level>> const & get_local_level_entries() const { return m_local_level_decls.get_entries(); }
+    /** \brief By default, when the parser finds a unknown identifier, it signs an error.
         This scope object temporarily changes this behavior. In any scope where this object
         is declared, the parse creates a constant even when the identifier is unknown.
         This behavior is useful when we are trying to parse mutually recursive declarations.
diff --git a/src/frontends/lean/util.cpp b/src/frontends/lean/util.cpp
index 53a2ccbf5..a4a14045a 100644
--- a/src/frontends/lean/util.cpp
+++ b/src/frontends/lean/util.cpp
@@ -114,6 +114,61 @@ expr mk_section_local_ref(name const & n, levels const & sec_ls, unsigned num_se
     return mk_implicit(mk_app(mk_explicit(mk_constant(n, sec_ls)), params));
 }
 
+bool is_section_local_ref(expr const & e) {
+    if (!is_implicit(e))
+        return false;
+    expr const & imp_arg = get_implicit_arg(e);
+    if (!is_app(imp_arg))
+        return false;
+    buffer<expr> locals;
+    expr const & f = get_app_args(imp_arg, locals);
+    return
+        is_explicit(f) &&
+        is_constant(get_explicit_arg(f)) &&
+        std::all_of(locals.begin(), locals.end(),
+                    [](expr const & l) {
+                        return is_explicit(l) && is_local(get_explicit_arg(l));
+                    });
+}
+
+expr update_section_local_ref(expr const & e, name_set const & lvls_to_remove, name_set const & locals_to_remove) {
+    lean_assert(is_section_local_ref(e));
+    if (locals_to_remove.empty() && lvls_to_remove.empty())
+        return e;
+    buffer<expr> locals;
+    expr const & f = get_app_args(get_implicit_arg(e), locals);
+    lean_assert(is_explicit(f));
+
+    expr new_f;
+    if (!lvls_to_remove.empty()) {
+        expr const & c = get_explicit_arg(f);
+        lean_assert(is_constant(c));
+        new_f = mk_explicit(update_constant(c, filter(const_levels(c), [&](level const & l) {
+                        return is_param(l) && !lvls_to_remove.contains(param_id(l));
+                    })));
+    } else {
+        new_f = f;
+    }
+
+    if (!locals_to_remove.empty()) {
+        unsigned j = 0;
+        for (unsigned i = 0; i < locals.size(); i++) {
+            expr const & l = locals[i];
+            if (!locals_to_remove.contains(mlocal_name(get_explicit_arg(l)))) {
+                locals[j] = l;
+                j++;
+            }
+        }
+        locals.shrink(j);
+    }
+
+    if (locals.empty()) {
+        return get_explicit_arg(new_f);
+    } else {
+        return mk_implicit(mk_app(new_f, locals));
+    }
+}
+
 expr Fun(buffer<expr> const & locals, expr const & e, parser & p) {
     bool use_cache = false;
     return p.rec_save_pos(Fun(locals, e, use_cache), p.pos_of(e));
diff --git a/src/frontends/lean/util.h b/src/frontends/lean/util.h
index 096c9dfdf..6fd0f6bd8 100644
--- a/src/frontends/lean/util.h
+++ b/src/frontends/lean/util.h
@@ -36,6 +36,21 @@ list<expr> locals_to_context(expr const & e, parser const & p);
     That is, when the user writes \c n inside the section she is really getting the term returned by this function.
 */
 expr mk_section_local_ref(name const & n, levels const & sec_ls, unsigned num_sec_params, expr const * sec_params);
+/** \brief Return true iff \c e is a term of the form
+    <tt>(@^-1 (@n.{ls} @l_1 ... @l_n))</tt> where
+    \c n is a constant and l_i's are local constants.
+
+    \remark is_section_local_ref(mk_section_local_ref(n, ls, num_ps, ps)) always hold.
+*/
+bool is_section_local_ref(expr const & e);
+/** \brief Given a term \c e s.t. is_section_local_ref(e) is true, remove all local constants in \c to_remove.
+    That is, if \c e is of the form
+    <tt>(@^-1 (@n.{u_1 ... u_k} @l_1 ... @l_n))</tt>
+    Then, return a term s.t.
+       1) any l_i s.t. mlocal_name(l_i) in \c locals_to_remove is removed.
+       2) any level u_j in \c lvls_to_remove is removed
+*/
+expr update_section_local_ref(expr const & e, name_set const & lvls_to_remove, name_set const & locals_to_remove);
 
 /** \brief Fun(locals, e), but also propagate \c e position to result */
 expr Fun(buffer<expr> const & locals, expr const & e, parser & p);
diff --git a/tests/lean/run/section4.lean b/tests/lean/run/section4.lean
new file mode 100644
index 000000000..b5676a8b1
--- /dev/null
+++ b/tests/lean/run/section4.lean
@@ -0,0 +1,20 @@
+import logic
+
+section
+  universe k
+  parameter A : Type
+
+  section
+    universe l
+    universe u
+    parameter B : Type
+    definition foo (a : A) (b : B) := b
+
+    inductive mypair :=
+    mk : A → B → mypair
+  end
+  variable a : A
+  check foo num a 0
+  definition pr1 (p : mypair num) : A   := mypair.rec (λ a b, a) p
+  definition pr2 (p : mypair num) : num := mypair.rec (λ a b, b) p
+end