diff --git a/src/library/CMakeLists.txt b/src/library/CMakeLists.txt
index ca6d01e08..abc9e13a0 100644
--- a/src/library/CMakeLists.txt
+++ b/src/library/CMakeLists.txt
@@ -19,4 +19,4 @@ add_library(library OBJECT deep_copy.cpp expr_lt.cpp io_state.cpp
   tmp_type_context.cpp fun_info_manager.cpp congr_lemma_manager.cpp
   abstract_expr_manager.cpp light_lt_manager.cpp trace.cpp
   attribute_manager.cpp error_handling.cpp unification_hint.cpp defeq_simp_lemmas.cpp
-  defeq_simplifier.cpp local_context.cpp)
+  defeq_simplifier.cpp proof_irrel_expr_manager.cpp local_context.cpp)
diff --git a/src/library/proof_irrel_expr_manager.cpp b/src/library/proof_irrel_expr_manager.cpp
new file mode 100644
index 000000000..3abc4a05f
--- /dev/null
+++ b/src/library/proof_irrel_expr_manager.cpp
@@ -0,0 +1,120 @@
+/*
+Copyright (c) 2015 Daniel Selsam. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Author: Daniel Selsam
+*/
+#include "library/proof_irrel_expr_manager.h"
+#include "kernel/instantiate.h"
+#include "util/safe_arith.h"
+#include "util/list_fn.h"
+
+namespace lean {
+
+unsigned proof_irrel_expr_manager::hash(expr const & e) {
+    unsigned h;
+    switch (e.kind()) {
+    case expr_kind::Constant:
+    case expr_kind::Local:
+    case expr_kind::Meta:
+    case expr_kind::Sort:
+    case expr_kind::Var:
+    case expr_kind::Macro:
+        return e.hash();
+    case expr_kind::Lambda:
+    case expr_kind::Pi:
+        h = hash(binding_domain(e));
+        // Remark binding_domain(e) may contain de-bruijn variables.
+        // We can instantiate them eagerly as we do here, or lazily.
+        // The lazy approach is potentially more efficient, but we would have
+        // to use something more sophisticated than an instantiate_rev at expr_kind::App
+        m_locals.push_back(instantiate_rev(m_tctx.mk_tmp_local(binding_domain(e)), m_locals.size(), m_locals.data()));
+        h = ::lean::hash(h, hash(binding_body(e)));
+        m_locals.pop_back();
+        return h;
+    case expr_kind::App:
+        buffer<expr> args;
+        expr const & f     = get_app_args(e, args);
+        unsigned prefix_sz = m_fun_info_manager.get_specialization_prefix_size(instantiate_rev(f, m_locals.size(), m_locals.data()), args.size());
+        expr new_f = e;
+        unsigned rest_sz   = args.size() - prefix_sz;
+        for (unsigned i = 0; i < rest_sz; i++)
+            new_f = app_fn(new_f);
+        new_f = instantiate_rev(new_f, m_locals.size(), m_locals.data());
+        h = hash(new_f);
+        fun_info info = m_fun_info_manager.get(new_f, rest_sz);
+        lean_assert(length(info.get_params_info()) == rest_sz);
+        unsigned i = prefix_sz;
+        for_each(info.get_params_info(), [&](param_info const & p_info) {
+                if (!p_info.is_prop()) {
+                    h = ::lean::hash(h, hash(args[i]));
+                }
+                i++;
+            });
+        return h;
+    }
+    lean_unreachable();
+}
+
+bool proof_irrel_expr_manager::is_equal(expr const & a, expr const & b) {
+    if (is_eqp(a, b))          return true;
+    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
+    case expr_kind::Constant: case expr_kind::Sort:
+        return a == 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:
+        if (!is_equal(binding_domain(a), binding_domain(b))) return false;
+        // see comment at proof_irrel_expr_manager::hash
+        m_locals.push_back(instantiate_rev(m_tctx.mk_tmp_local(binding_domain(a)), m_locals.size(), m_locals.data()));
+        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;
+        for (unsigned i = 0; i < macro_num_args(a); i++) {
+            if (!is_equal(macro_arg(a, i), macro_arg(b, i)))
+                return false;
+        }
+        return true;
+    case expr_kind::App:
+        buffer<expr> a_args, b_args;
+        expr const & f_a   = get_app_args(a, a_args);
+        expr const & 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;
+        unsigned prefix_sz = m_fun_info_manager.get_specialization_prefix_size(instantiate_rev(f_a, m_locals.size(), m_locals.data()), a_args.size());
+        for (unsigned i = 0; i < prefix_sz; i++) {
+            if (!is_equal(a_args[i], b_args[i]))
+                return false;
+        }
+        expr new_f_a       = a;
+        unsigned rest_sz   = a_args.size() - prefix_sz;
+        for (unsigned i = 0; i < rest_sz; i++) {
+            new_f_a = app_fn(new_f_a);
+        }
+        new_f_a = instantiate_rev(new_f_a, m_locals.size(), m_locals.data());
+        fun_info info = m_fun_info_manager.get(new_f_a, rest_sz);
+        bool not_equal = false;
+        lean_assert(length(info.get_params_info()) == rest_sz);
+        unsigned i = prefix_sz;
+        for_each(info.get_params_info(), [&](param_info const & p_info) {
+                    if (not_equal)
+                        return;
+                    if (!p_info.is_prop() && !is_equal(a_args[i], b_args[i])) {
+                        not_equal = true;
+                    }
+                    i++;
+            });
+        return !not_equal;
+    }
+    lean_unreachable(); // LCOV_EXCL_LINE
+}
+}
diff --git a/src/library/proof_irrel_expr_manager.h b/src/library/proof_irrel_expr_manager.h
new file mode 100644
index 000000000..0cde40908
--- /dev/null
+++ b/src/library/proof_irrel_expr_manager.h
@@ -0,0 +1,31 @@
+/*
+Copyright (c) 2015 Daniel Selsam. All rights reserved.
+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/fun_info_manager.h"
+
+namespace lean {
+
+/** \brief Proof-irrelevant expression manager, to allow comparing expressions while ignoring proofs. */
+
+class proof_irrel_expr_manager {
+    /* The [fun_info_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 [fun_info_manager], which we
+       expect to be very small in general. */
+    std::vector<expr>     m_locals;
+    type_context        & m_tctx;
+    fun_info_manager    & m_fun_info_manager;
+public:
+    proof_irrel_expr_manager(fun_info_manager & f_info_manager):
+        m_tctx(f_info_manager.ctx()), m_fun_info_manager(f_info_manager) {}
+    unsigned hash(expr const & e);
+    bool is_equal(expr const & a, expr const & b);
+};
+
+}