diff --git a/src/frontends/lean/decl_cmds.cpp b/src/frontends/lean/decl_cmds.cpp
index 7b91b5586..fc886a4dd 100644
--- a/src/frontends/lean/decl_cmds.cpp
+++ b/src/frontends/lean/decl_cmds.cpp
@@ -362,10 +362,8 @@ environment definition_cmd_core(parser & p, bool is_theorem, bool is_opaque, boo
         ls = to_list(ls_buffer.begin(), ls_buffer.end());
         levels section_ls = collect_section_nonvar_levels(p, ls);
         remove_section_variables(p, section_ps);
-        for (expr & param : section_ps)
-            param = mk_explicit(param);
         if (!section_ps.empty()) {
-            expr ref = mk_implicit(mk_app(mk_explicit(mk_constant(real_n, section_ls)), section_ps));
+            expr ref = mk_section_local_ref(real_n, section_ls, section_ps.size(), section_ps.data());
             p.add_local_expr(n, ref);
         } else if (section_ls) {
             expr ref = mk_constant(real_n, section_ls);
diff --git a/src/frontends/lean/inductive_cmd.cpp b/src/frontends/lean/inductive_cmd.cpp
index 400831a04..ac82376eb 100644
--- a/src/frontends/lean/inductive_cmd.cpp
+++ b/src/frontends/lean/inductive_cmd.cpp
@@ -594,9 +594,7 @@ struct inductive_cmd_fn {
         else
             id = name(full_id.get_string());
         if (in_section_or_context(env)) {
-            expr r = mk_explicit(mk_constant(full_id, section_levels));
-            r = mk_app(r, section_params);
-            r = mk_implicit(r);
+            expr r = mk_section_local_ref(full_id, section_levels, section_params.size(), section_params.data());
             m_p.add_local_expr(id, r);
         }
         if (full_id != id)
diff --git a/src/frontends/lean/util.cpp b/src/frontends/lean/util.cpp
index 155ef4e95..53a2ccbf5 100644
--- a/src/frontends/lean/util.cpp
+++ b/src/frontends/lean/util.cpp
@@ -107,6 +107,13 @@ list<expr> locals_to_context(expr const & e, parser const & p) {
     return to_list(locals.begin(), locals.end());
 }
 
+expr mk_section_local_ref(name const & n, levels const & sec_ls, unsigned num_sec_params, expr const * sec_params) {
+    buffer<expr> params;
+    for (unsigned i = 0; i < num_sec_params; i++)
+        params.push_back(mk_explicit(sec_params[i]));
+    return mk_implicit(mk_app(mk_explicit(mk_constant(n, sec_ls)), params));
+}
+
 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 77a7294c3..096c9dfdf 100644
--- a/src/frontends/lean/util.h
+++ b/src/frontends/lean/util.h
@@ -31,6 +31,12 @@ void sort_section_params(expr_struct_set const & locals, parser const & p, buffe
 /** \brief Remove from \c ps local constants that are tagged as section variables. */
 void remove_section_variables(parser const & p, buffer<expr> & ps);
 list<expr> locals_to_context(expr const & e, parser const & p);
+/** \brief Create the term <tt>(@^-1 (@n.{sec_ls} @sec_params[0] ... @sec_params[num_sec_params-1]))</tt>
+    When we declare \c n inside of a section, the section parameters and universes are fixes.
+    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 Fun(locals, e), but also propagate \c e position to result */
 expr Fun(buffer<expr> const & locals, expr const & e, parser & p);
 /** \brief Pi(locals, e), but also propagate \c e position to result */