diff --git a/library/init/default.lean b/library/init/default.lean
index 1f1ea1bd72..c8d58969df 100644
--- a/library/init/default.lean
+++ b/library/init/default.lean
@@ -12,4 +12,5 @@ import init.monad init.option init.state init.fin init.list init.char init.strin
 import init.monad_combinators init.set
 import init.timeit init.trace init.unsigned init.ordering init.list_classes init.coe
 import init.wf init.nat_div init.meta init.instances init.breakpoint
-import init.sigma_lex init.id_locked init.order init.algebra init.nat_lemmas init.char_lemmas
+import init.sigma_lex init.id_locked init.order init.algebra
+import init.nat_lemmas init.char_lemmas init.string_lemmas
diff --git a/library/init/string_lemmas.lean b/library/init/string_lemmas.lean
new file mode 100644
index 0000000000..5cac68a026
--- /dev/null
+++ b/library/init/string_lemmas.lean
@@ -0,0 +1,21 @@
+/-
+Copyright (c) 2016 Microsoft Corporation. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Author: Leonardo de Moura
+-/
+prelude
+import init.meta
+
+namespace string
+lemma empty_ne_str (c : char) (s : string) : empty ≠ str c s :=
+begin intro h, contradiction end
+
+lemma str_ne_empty (c : char) (s : string) : str c s ≠ empty :=
+begin intro h, contradiction end
+
+lemma str_ne_str_left {c₁ c₂ : char} (s₁ s₂ : string) : c₁ ≠ c₂ → str c₁ s₁ ≠ str c₂ s₂ :=
+begin intros h₁ h₂, unfold str at h₂, injection h₂, contradiction end
+
+lemma str_ne_str_right (c₁ c₂ : char) {s₁ s₂ : string} : s₁ ≠ s₂ → str c₁ s₁ ≠ str c₂ s₂ :=
+begin intros h₁ h₂, unfold str at h₂, injection h₂, contradiction end
+end string
diff --git a/src/library/comp_val.cpp b/src/library/comp_val.cpp
index 086a6e378c..123623cae9 100644
--- a/src/library/comp_val.cpp
+++ b/src/library/comp_val.cpp
@@ -5,6 +5,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Author: Leonardo de Moura
 */
 #include "library/num.h"
+#include "library/string.h"
 #include "library/util.h"
 #include "library/constants.h"
 
@@ -113,7 +114,7 @@ optional<expr> mk_fin_val_ne_proof(expr const & a, expr const & b) {
     expr const & n   = app_arg(app_fn(app_fn(a)));
     expr const & v_a = app_arg(app_fn(a));
     expr const & v_b = app_arg(app_fn(b));
-    auto pr = mk_nat_val_lt_proof(v_a, v_b);
+    auto pr = mk_nat_val_ne_proof(v_a, v_b);
     if (!pr) return none_expr();
     return some_expr(mk_app(mk_constant(get_fin_ne_of_vne_name()), n, a, b, *pr));
 }
@@ -134,8 +135,51 @@ optional<expr> mk_char_val_ne_proof(expr const & a, expr const & b) {
     return mk_fin_val_ne_proof(a, b);
 }
 
+/* Remark: this function assumes 'e' has type string */
+static bool is_string_str(expr const & e, expr & c, expr & s) {
+    if (is_app_of(e, get_string_str_name(), 2) ||
+        is_app_of(e, get_list_cons_name(), 3)) {
+        c = app_arg(app_fn(e));
+        s = app_arg(e);
+        return true;
+    }
+    return false;
+}
+
+/* Remark: this function assumes 'e' has type string */
+static bool is_string_empty(expr const & e) {
+    return
+        is_constant(e, get_string_empty_name()) ||
+        is_app_of(e, get_list_nil_name(), 1);
+}
+
+optional<expr> mk_string_val_ne_proof(expr a, expr b) {
+    if (auto new_a = expand_string_macro(a))
+        a = *new_a;
+    if (auto new_b = expand_string_macro(b))
+        b = *new_b;
+    expr c_a, s_a;
+    expr c_b, s_b;
+    if (is_string_str(a, c_a, s_a)) {
+        if (is_string_str(b, c_b, s_b)) {
+            if (auto pr = mk_char_val_ne_proof(c_a, c_b)) {
+                return some_expr(mk_app({mk_constant(get_string_str_ne_str_left_name()), c_a, c_b, s_a, s_b, *pr}));
+            } else if (auto pr = mk_string_val_ne_proof(s_a, s_b)) {
+                return some_expr(mk_app({mk_constant(get_string_str_ne_str_right_name()), c_a, c_b, s_a, s_b, *pr}));
+            }
+        } else if (is_string_empty(b)) {
+            return some_expr(mk_app(mk_constant(get_string_str_ne_empty_name()), c_a, s_a));
+        }
+    } else if (is_string_empty(a)) {
+        if (is_string_str(b, c_b, s_b)) {
+            return some_expr(mk_app(mk_constant(get_string_empty_ne_str_name()), c_b, s_b));
+        }
+    }
+    return none_expr();
+}
+
 void initialize_comp_val() {
-    g_char_sz = new expr(to_nat_expr(mpz(255)));
+    g_char_sz = new expr(to_nat_expr(mpz(256)));
 }
 
 void finalize_comp_val() {
diff --git a/src/library/comp_val.h b/src/library/comp_val.h
index d84b25b198..5f79fc3e71 100644
--- a/src/library/comp_val.h
+++ b/src/library/comp_val.h
@@ -34,6 +34,9 @@ optional<expr> mk_fin_val_ne_proof(expr const & a, expr const & b);
 /* Similar to mk_char_val_ne_proof, but for char type */
 optional<expr> mk_char_val_ne_proof(expr const & a, expr const & b);
 
+/* Similar to mk_char_val_ne_proof, but for string type */
+optional<expr> mk_string_val_ne_proof(expr a, expr b);
+
 void initialize_comp_val();
 void finalize_comp_val();
 }
diff --git a/src/library/constants.cpp b/src/library/constants.cpp
index 09206c0fdb..72ef950770 100644
--- a/src/library/constants.cpp
+++ b/src/library/constants.cpp
@@ -359,6 +359,10 @@ name const * g_store = nullptr;
 name const * g_string = nullptr;
 name const * g_string_empty = nullptr;
 name const * g_string_str = nullptr;
+name const * g_string_empty_ne_str = nullptr;
+name const * g_string_str_ne_empty = nullptr;
+name const * g_string_str_ne_str_left = nullptr;
+name const * g_string_str_ne_str_right = nullptr;
 name const * g_sub = nullptr;
 name const * g_subsingleton = nullptr;
 name const * g_subsingleton_elim = nullptr;
@@ -778,6 +782,10 @@ void initialize_constants() {
     g_string = new name{"string"};
     g_string_empty = new name{"string", "empty"};
     g_string_str = new name{"string", "str"};
+    g_string_empty_ne_str = new name{"string", "empty_ne_str"};
+    g_string_str_ne_empty = new name{"string", "str_ne_empty"};
+    g_string_str_ne_str_left = new name{"string", "str_ne_str_left"};
+    g_string_str_ne_str_right = new name{"string", "str_ne_str_right"};
     g_sub = new name{"sub"};
     g_subsingleton = new name{"subsingleton"};
     g_subsingleton_elim = new name{"subsingleton", "elim"};
@@ -1198,6 +1206,10 @@ void finalize_constants() {
     delete g_string;
     delete g_string_empty;
     delete g_string_str;
+    delete g_string_empty_ne_str;
+    delete g_string_str_ne_empty;
+    delete g_string_str_ne_str_left;
+    delete g_string_str_ne_str_right;
     delete g_sub;
     delete g_subsingleton;
     delete g_subsingleton_elim;
@@ -1617,6 +1629,10 @@ name const & get_store_name() { return *g_store; }
 name const & get_string_name() { return *g_string; }
 name const & get_string_empty_name() { return *g_string_empty; }
 name const & get_string_str_name() { return *g_string_str; }
+name const & get_string_empty_ne_str_name() { return *g_string_empty_ne_str; }
+name const & get_string_str_ne_empty_name() { return *g_string_str_ne_empty; }
+name const & get_string_str_ne_str_left_name() { return *g_string_str_ne_str_left; }
+name const & get_string_str_ne_str_right_name() { return *g_string_str_ne_str_right; }
 name const & get_sub_name() { return *g_sub; }
 name const & get_subsingleton_name() { return *g_subsingleton; }
 name const & get_subsingleton_elim_name() { return *g_subsingleton_elim; }
diff --git a/src/library/constants.h b/src/library/constants.h
index 5ba90e9cdb..15e9dd37a6 100644
--- a/src/library/constants.h
+++ b/src/library/constants.h
@@ -361,6 +361,10 @@ name const & get_store_name();
 name const & get_string_name();
 name const & get_string_empty_name();
 name const & get_string_str_name();
+name const & get_string_empty_ne_str_name();
+name const & get_string_str_ne_empty_name();
+name const & get_string_str_ne_str_left_name();
+name const & get_string_str_ne_str_right_name();
 name const & get_sub_name();
 name const & get_subsingleton_name();
 name const & get_subsingleton_elim_name();
diff --git a/src/library/constants.txt b/src/library/constants.txt
index cf60936215..7f4a93d73b 100644
--- a/src/library/constants.txt
+++ b/src/library/constants.txt
@@ -354,6 +354,10 @@ store
 string
 string.empty
 string.str
+string.empty_ne_str
+string.str_ne_empty
+string.str_ne_str_left
+string.str_ne_str_right
 sub
 subsingleton
 subsingleton.elim
diff --git a/src/library/string.cpp b/src/library/string.cpp
index ffcbf4b815..52cb993191 100644
--- a/src/library/string.cpp
+++ b/src/library/string.cpp
@@ -139,6 +139,11 @@ void initialize_string() {
                                 });
 }
 
+optional<expr> expand_string_macro(expr const & e) {
+    if (!is_string_macro(e)) return none_expr();
+    return some_expr(from_string_core(to_string_macro(e).get_value()));
+}
+
 void finalize_string() {
     delete g_nat;
     delete g_str;
diff --git a/src/library/string.h b/src/library/string.h
index 70743be21e..7c466f6925 100644
--- a/src/library/string.h
+++ b/src/library/string.h
@@ -18,6 +18,8 @@ expr from_string(std::string const & s);
 optional<std::string> to_string(expr const & e);
 
 bool is_string_macro(expr const & e);
+/** \brief Expand string macro if 'e' is a string macro */
+optional<expr> expand_string_macro(expr const & e);
 
 optional<char> to_char(expr const & e);