diff --git a/src/library/abstract_expr_manager.cpp b/src/library/abstract_expr_manager.cpp
index 8d93a0a12..f49e3f8d7 100644
--- a/src/library/abstract_expr_manager.cpp
+++ b/src/library/abstract_expr_manager.cpp
@@ -4,12 +4,14 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Author: Daniel Selsam
 */
 #include "library/abstract_expr_manager.h"
+#include "kernel/instantiate.h"
 #include "util/safe_arith.h"
 #include "util/list_fn.h"
 
 namespace lean {
 
 unsigned abstract_expr_manager::hash(expr const & e) {
+    unsigned h;
     switch (e.kind()) {
     case expr_kind::Constant:
     case expr_kind::Local:
@@ -20,12 +22,16 @@ unsigned abstract_expr_manager::hash(expr const & e) {
         return e.hash();
     case expr_kind::Lambda:
     case expr_kind::Pi:
-        return ::lean::hash(hash(binding_domain(e)), hash(binding_body(e)));
+        h = hash(binding_domain(e));
+        m_locals.push_back(m_tctx.mk_tmp_local(binding_domain(e)));
+        h = ::lean::hash(h, hash(binding_body(e)));
+        m_locals.pop_back();
+        return h;
     case expr_kind::App:
         buffer<expr> args;
-        expr f = get_app_args(e, args);
+        expr f = instantiate_rev(get_app_args(e, args), m_locals.size(), m_locals.data());
         optional<congr_lemma> f_congr = m_congr_lemma_manager.mk_congr(f, args.size());
-        unsigned h = hash(f);
+        h = hash(f);
         if (!f_congr) {
             for (expr const & arg : args) h = ::lean::hash(h, hash(arg));
         } else {
@@ -46,6 +52,7 @@ bool abstract_expr_manager::is_equal(expr const & a, expr const & b) {
         if (hash(a) != hash(b))    return false;
         if (a.kind() != b.kind())  return false;
         if (is_var(a))             return var_idx(a) == var_idx(b);
+        bool is_eq;
         switch (a.kind()) {
         case expr_kind::Var:
             lean_unreachable(); // LCOV_EXCL_LINE
@@ -54,7 +61,11 @@ bool abstract_expr_manager::is_equal(expr const & a, expr const & b) {
         case expr_kind::Meta: case expr_kind::Local:
             return mlocal_name(a) == mlocal_name(b) && is_equal(mlocal_type(a), mlocal_type(b));
         case expr_kind::Lambda: case expr_kind::Pi:
-            return is_equal(binding_domain(a), binding_domain(b)) && is_equal(binding_body(a), binding_body(b));
+            if (!is_equal(binding_domain(a), binding_domain(b))) return false;
+            m_locals.push_back(m_tctx.mk_tmp_local(binding_domain(a)));
+            is_eq = is_equal(binding_body(a), binding_body(b));
+            m_locals.pop_back();
+            return is_eq;
         case expr_kind::Macro:
             if (macro_def(a) != macro_def(b) || macro_num_args(a) != macro_num_args(b))
                 return false;
@@ -69,7 +80,8 @@ bool abstract_expr_manager::is_equal(expr const & a, expr const & b) {
             expr f_b = get_app_args(b, b_args);
             if (!is_equal(f_a, f_b)) return false;
             if (a_args.size() != b_args.size()) return false;
-            optional<congr_lemma> f_congr = m_congr_lemma_manager.mk_congr(f_a, a_args.size());
+            expr f = instantiate_rev(f_a, m_locals.size(), m_locals.data());
+            optional<congr_lemma> f_congr = m_congr_lemma_manager.mk_congr(f, a_args.size());
             bool not_equal = false;
             if (!f_congr) {
                 for (unsigned i = 0; i < a_args.size(); ++i) {
diff --git a/src/library/abstract_expr_manager.h b/src/library/abstract_expr_manager.h
index f80337fbc..556c7327b 100644
--- a/src/library/abstract_expr_manager.h
+++ b/src/library/abstract_expr_manager.h
@@ -4,7 +4,9 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Author: Daniel Selsam
 */
 #pragma once
+#include <vector>
 #include "kernel/expr.h"
+#include "library/type_context.h"
 #include "library/congr_lemma_manager.h"
 
 namespace lean {
@@ -12,9 +14,16 @@ namespace lean {
 /** \brief Abstract expression manager, to allow comparing expressions while ignoring subsingletons. */
 
 class abstract_expr_manager {
+    /* The [congr_lemma_manager] cannot handle [Var]s since it needs to infer types, and we do not
+       want to instantiate eagerly for performance reasons. Therefore we track the context ourselves,
+       and only instantiate on the expressions we pass to the [congr_lemma_manager], which we
+       expect to be very small in general. */
+    std::vector<expr>     m_locals;
+    type_context        & m_tctx;
     congr_lemma_manager & m_congr_lemma_manager;
 public:
-    abstract_expr_manager(congr_lemma_manager & c_lemma_manager): m_congr_lemma_manager(c_lemma_manager) {}
+    abstract_expr_manager(congr_lemma_manager & c_lemma_manager):
+        m_tctx(c_lemma_manager.ctx()), m_congr_lemma_manager(c_lemma_manager) {}
     unsigned hash(expr const & e);
     bool is_equal(expr const & a, expr const & b);
 };
diff --git a/src/library/congr_lemma_manager.cpp b/src/library/congr_lemma_manager.cpp
index 512656194..4f07f9542 100644
--- a/src/library/congr_lemma_manager.cpp
+++ b/src/library/congr_lemma_manager.cpp
@@ -301,6 +301,8 @@ public:
         m_builder(b), m_fmanager(fm), m_ctx(fm.ctx()),
         m_relation_info_getter(mk_relation_info_getter(fm.ctx().env())) {}
 
+    type_context & ctx() { return m_ctx; }
+
     optional<result> mk_congr_simp(expr const & fn) {
         fun_info finfo = m_fmanager.get(fn);
         return mk_congr_simp(fn, finfo.get_arity());
@@ -493,6 +495,8 @@ congr_lemma_manager::congr_lemma_manager(app_builder & b, fun_info_manager & fm)
 congr_lemma_manager::~congr_lemma_manager() {
 }
 
+type_context & congr_lemma_manager::ctx() { return m_ptr->ctx(); }
+
 auto congr_lemma_manager::mk_congr_simp(expr const & fn) -> optional<result> {
     return m_ptr->mk_congr_simp(fn);
 }
diff --git a/src/library/congr_lemma_manager.h b/src/library/congr_lemma_manager.h
index 37461ad67..e912a0df3 100644
--- a/src/library/congr_lemma_manager.h
+++ b/src/library/congr_lemma_manager.h
@@ -33,6 +33,8 @@ public:
     ~congr_lemma_manager();
     typedef congr_lemma result;
 
+    type_context & ctx();
+
     optional<result> mk_congr_simp(expr const & fn);
     optional<result> mk_congr_simp(expr const & fn, unsigned nargs);