diff --git a/src/library/CMakeLists.txt b/src/library/CMakeLists.txt
index dd124d94b4..498a524120 100644
--- a/src/library/CMakeLists.txt
+++ b/src/library/CMakeLists.txt
@@ -14,7 +14,7 @@ add_library(library OBJECT deep_copy.cpp expr_lt.cpp io_state.cpp
   local_context.cpp metavar_context.cpp type_context.cpp export_decl.cpp delayed_abstraction.cpp
   fun_info.cpp congr_lemma.cpp defeq_canonizer.cpp scope_pos_info_provider.cpp
   inductive.cpp mpq_macro.cpp arith_instance_manager.cpp replace_visitor_with_tc.cpp
-  aux_definition.cpp injectivity.cpp
+  aux_definition.cpp inverse.cpp
 
   # Legacy -- The following files will be eventually deleted
   normalize.cpp justification.cpp constraint.cpp metavar.cpp choice.cpp locals.cpp
diff --git a/src/library/init_module.cpp b/src/library/init_module.cpp
index 51baa5fbfa..4e51bb5ba7 100644
--- a/src/library/init_module.cpp
+++ b/src/library/init_module.cpp
@@ -49,7 +49,7 @@ Author: Leonardo de Moura
 #include "library/inductive.h"
 #include "library/mpq_macro.h"
 #include "library/arith_instance_manager.h"
-#include "library/injectivity.h"
+#include "library/inverse.h"
 
 // #include "library/congr_lemma_manager.h"
 // #include "library/light_lt_manager.h"
@@ -130,11 +130,11 @@ void initialize_library_module() {
     initialize_library_inductive();
     initialize_mpq_macro();
     initialize_arith_instance_manager();
-    initialize_injectivity();
+    initialize_inverse();
 }
 
 void finalize_library_module() {
-    finalize_injectivity();
+    finalize_inverse();
     finalize_arith_instance_manager();
     finalize_mpq_macro();
     finalize_library_inductive();
diff --git a/src/library/injectivity.cpp b/src/library/inverse.cpp
similarity index 54%
rename from src/library/injectivity.cpp
rename to src/library/inverse.cpp
index c4ef8bfb92..2f6273ab23 100644
--- a/src/library/injectivity.cpp
+++ b/src/library/inverse.cpp
@@ -9,38 +9,38 @@ Author: Leonardo de Moura
 #include "library/util.h"
 #include "library/scoped_ext.h"
 #include "library/attribute_manager.h"
-#include "library/injectivity.h"
+#include "library/inverse.h"
 
 namespace lean {
-struct injectivity_entry {
-    name             m_fn;
-    injectivity_info m_info;
-    injectivity_entry() {}
-    injectivity_entry(name const & fn, injectivity_info const & info):
+struct inverse_entry {
+    name         m_fn;
+    inverse_info m_info;
+    inverse_entry() {}
+    inverse_entry(name const & fn, inverse_info const & info):
         m_fn(fn), m_info(info) {}
 };
 
-struct injectivity_state {
-    name_map<injectivity_info> m_fn_info;  /* mapping from function to its inverse and lemma */
-    name_map<name>             m_inv_info; /* mapping from inverse to function */
+struct inverse_state {
+    name_map<inverse_info> m_fn_info;  /* mapping from function to its inverse and lemma */
+    name_map<name>         m_inv_info; /* mapping from inverse to function */
 
-    void add(injectivity_entry const & e) {
+    void add(inverse_entry const & e) {
         m_fn_info.insert(e.m_fn, e.m_info);
         m_inv_info.insert(e.m_info.m_inv, e.m_fn);
     }
 };
 
-static name * g_injectivity_name = nullptr;
+static name * g_inverse_name = nullptr;
 static std::string * g_key = nullptr;
 
-struct injectivity_config {
-    typedef injectivity_state state;
-    typedef injectivity_entry entry;
+struct inverse_config {
+    typedef inverse_state state;
+    typedef inverse_entry entry;
     static void add_entry(environment const &, io_state const &, state & s, entry const & e) {
         s.add(e);
     }
     static name const & get_class_name() {
-        return *g_injectivity_name;
+        return *g_inverse_name;
     }
     static std::string const & get_serialization_key() {
         return *g_key;
@@ -58,68 +58,69 @@ struct injectivity_config {
     }
 };
 
-template class scoped_ext<injectivity_config>;
-typedef scoped_ext<injectivity_config> injectivity_ext;
+template class scoped_ext<inverse_config>;
+typedef scoped_ext<inverse_config> inverse_ext;
 
-optional<injectivity_info> has_inverse(environment const & env, name const & fn) {
-    if (auto r = injectivity_ext::get_state(env).m_fn_info.find(fn))
-        return optional<injectivity_info>(*r);
+optional<inverse_info> has_inverse(environment const & env, name const & fn) {
+    if (auto r = inverse_ext::get_state(env).m_fn_info.find(fn))
+        return optional<inverse_info>(*r);
     else
-        return optional<injectivity_info>();
+        return optional<inverse_info>();
 }
 
 optional<name> is_inverse(environment const & env, name const & inv) {
-    if (auto r = injectivity_ext::get_state(env).m_inv_info.find(inv))
+    if (auto r = inverse_ext::get_state(env).m_inv_info.find(inv))
         return optional<name>(*r);
     else
         return optional<name>();
 }
 
-void throw_injectivity_error() {
-    throw exception("invalid injectivity lemma, "
+void throw_inverse_error() {
+    throw exception("invalid inverse lemma, "
                     "it should be of the form: (f ... (g ... x)) = x");
 }
 
-environment add_injectivity_lemma(environment const & env, name const & lemma, bool persistent) {
+environment add_inverse_lemma(environment const & env, name const & lemma, bool persistent) {
     type_checker tc(env);
     declaration d = env.get(lemma);
     buffer<expr> tele;
     expr type     = to_telescope(tc, d.get_type(), tele);
     expr lhs, rhs;
     if (!is_eq(type, lhs, rhs) || !is_app(lhs) || !is_constant(get_app_fn(lhs)) || !is_local(rhs))
-        throw_injectivity_error();
-    injectivity_info info;
+        throw_inverse_error();
+    inverse_info info;
     buffer<expr> lhs_args;
     expr const & lhs_fn = get_app_args(lhs, lhs_args);
-    info.m_inv   = const_name(lhs_fn);
-    info.m_lemma = lemma;
+    info.m_inv       = const_name(lhs_fn);
+    info.m_inv_arity = lhs_args.size();
+    info.m_lemma     = lemma;
     expr const & last_arg = lhs_args.back();
     if (!is_app(last_arg) || !is_constant(get_app_fn(last_arg)))
-        throw_injectivity_error();
+        throw_inverse_error();
     buffer<expr> last_arg_args;
     expr const & fn = get_app_args(last_arg, last_arg_args);
     if (last_arg_args.back() != rhs)
-        throw_injectivity_error();
+        throw_inverse_error();
     info.m_arity = last_arg_args.size();
-    return injectivity_ext::add_entry(env, get_dummy_ios(), injectivity_entry(const_name(fn), info), persistent);
+    return inverse_ext::add_entry(env, get_dummy_ios(), inverse_entry(const_name(fn), info), persistent);
 }
 
-void initialize_injectivity() {
-    g_injectivity_name = new name("injectivity");
-    g_key = new std::string("injectivity");
-    injectivity_ext::initialize();
+void initialize_inverse() {
+    g_inverse_name = new name("inverse");
+    g_key = new std::string("inverse");
+    inverse_ext::initialize();
 
-    register_system_attribute(basic_attribute("injectivity", "attribute for marking injectivity lemmas "
+    register_system_attribute(basic_attribute("inverse", "attribute for marking inverse lemmas "
                                               "used by the equation compiler",
                                               [](environment const & env, io_state const &, name const & d, unsigned,
                                                  bool persistent) {
-                                                  return add_injectivity_lemma(env, d, persistent);
+                                                  return add_inverse_lemma(env, d, persistent);
                                               }));
 }
 
-void finalize_injectivity() {
-    injectivity_ext::finalize();
+void finalize_inverse() {
+    inverse_ext::finalize();
     delete g_key;
-    delete g_injectivity_name;
+    delete g_inverse_name;
 }
 }
diff --git a/src/library/injectivity.h b/src/library/inverse.h
similarity index 57%
rename from src/library/injectivity.h
rename to src/library/inverse.h
index 5ce1ade3a2..b5dbfe006e 100644
--- a/src/library/injectivity.h
+++ b/src/library/inverse.h
@@ -8,15 +8,16 @@ Author: Leonardo de Moura
 #include "kernel/environment.h"
 
 namespace lean {
-struct injectivity_info {
+struct inverse_info {
     unsigned m_arity;
     name     m_inv;
+    unsigned m_inv_arity;
     name     m_lemma;
 };
 
-optional<injectivity_info> has_inverse(environment const & env, name const & fn);
+optional<inverse_info> has_inverse(environment const & env, name const & fn);
 optional<name> is_inverse(environment const & env, name const & inv);
-environment add_injectivity_lemma(environment const & env, name const & lemma, bool persistent);
-void initialize_injectivity();
-void finalize_injectivity();
+environment add_inverse_lemma(environment const & env, name const & lemma, bool persistent);
+void initialize_inverse();
+void finalize_inverse();
 }