diff --git a/src/library/simplifier/simplifier.cpp b/src/library/simplifier/simplifier.cpp
index 119418573..82a30d325 100644
--- a/src/library/simplifier/simplifier.cpp
+++ b/src/library/simplifier/simplifier.cpp
@@ -38,6 +38,10 @@ Author: Leonardo de Moura
 #define LEAN_SIMPLIFIER_UNFOLD false
 #endif
 
+#ifndef LEAN_SIMPLIFIER_CONDITIONAL
+#define LEAN_SIMPLIFIER_CONDITIONAL true
+#endif
+
 #ifndef LEAN_SIMPLIFIER_MAX_STEPS
 #define LEAN_SIMPLIFIER_MAX_STEPS std::numeric_limits<unsigned>::max()
 #endif
@@ -48,6 +52,7 @@ static name g_simplifier_contextual   {"simplifier", "contextual"};
 static name g_simplifier_single_pass  {"simplifier", "single_pass"};
 static name g_simplifier_beta         {"simplifier", "beta"};
 static name g_simplifier_unfold       {"simplifier", "unfold"};
+static name g_simplifier_conditional  {"simplifier", "conditional"};
 static name g_simplifier_max_steps    {"simplifier", "max_steps"};
 
 RegisterBoolOption(g_simplifier_proofs, LEAN_SIMPLIFIER_PROOFS, "(simplifier) generate proofs");
@@ -55,6 +60,7 @@ RegisterBoolOption(g_simplifier_contextual, LEAN_SIMPLIFIER_CONTEXTUAL, "(simpli
 RegisterBoolOption(g_simplifier_single_pass, LEAN_SIMPLIFIER_SINGLE_PASS, "(simplifier) if false then the simplifier keeps applying simplifications as long as possible");
 RegisterBoolOption(g_simplifier_beta, LEAN_SIMPLIFIER_BETA, "(simplifier) use beta-reductions");
 RegisterBoolOption(g_simplifier_unfold, LEAN_SIMPLIFIER_UNFOLD, "(simplifier) unfolds non-opaque definitions");
+RegisterBoolOption(g_simplifier_conditional, LEAN_SIMPLIFIER_CONDITIONAL, "(simplifier) conditional rewriting");
 RegisterUnsignedOption(g_simplifier_max_steps, LEAN_SIMPLIFIER_MAX_STEPS, "(simplifier) maximum number of steps");
 
 bool get_simplifier_proofs(options const & opts) {
@@ -72,6 +78,9 @@ bool get_simplifier_beta(options const & opts) {
 bool get_simplifier_unfold(options const & opts) {
     return opts.get_bool(g_simplifier_unfold, LEAN_SIMPLIFIER_UNFOLD);
 }
+bool get_simplifier_conditional(options const & opts) {
+    return opts.get_bool(g_simplifier_conditional, LEAN_SIMPLIFIER_CONDITIONAL);
+}
 unsigned get_simplifier_max_steps(options const & opts) {
     return opts.get_unsigned(g_simplifier_max_steps, LEAN_SIMPLIFIER_MAX_STEPS);
 }
@@ -90,6 +99,7 @@ class simplifier_fn {
     bool           m_single_pass;
     bool           m_beta;
     bool           m_unfold;
+    bool           m_conditional;
     unsigned       m_max_steps;
 
     struct match_fn {
@@ -106,8 +116,12 @@ class simplifier_fn {
         expr           m_out;
         optional<expr> m_proof;
         bool           m_heq_proof;
-        explicit result(expr const & out, bool heq_proof = false):m_out(out), m_heq_proof(heq_proof) {}
-        result(expr const & out, expr const & pr, bool heq_proof = false):m_out(out), m_proof(pr), m_heq_proof(heq_proof) {}
+        explicit result(expr const & out, bool heq_proof = false):
+            m_out(out), m_heq_proof(heq_proof) {}
+        result(expr const & out, expr const & pr, bool heq_proof = false):
+            m_out(out), m_proof(pr), m_heq_proof(heq_proof) {}
+        result(expr const & out, optional<expr> const & pr, bool heq_proof = false):
+            m_out(out), m_proof(pr), m_heq_proof(heq_proof) {}
     };
 
     struct set_context {
@@ -294,9 +308,9 @@ class simplifier_fn {
         }
 
         if (!changed) {
-            return rewrite(e, result(e));
+            return rewrite_app(e, result(e));
         } else if (!m_proofs_enabled) {
-            return rewrite(e, result(mk_app(new_args)));
+            return rewrite_app(e, result(mk_app(new_args)));
         } else {
             expr out = mk_app(new_args);
             unsigned i = 0;
@@ -310,7 +324,7 @@ class simplifier_fn {
             bool heq_proof = false;
             if (i == 0) {
                 pr = *(proofs[0]);
-                heq_proof = heq_proofs[0];
+                heq_proof = m_has_heq && heq_proofs[0];
             } else if (m_has_heq && heq_proofs[i]) {
                 expr f = mk_app_prefix(i, new_args);
                 pr = mk_hcongr_th(f_types[i-1], f_types[i-1], f, f, arg(e, i), new_args[i],
@@ -341,10 +355,17 @@ class simplifier_fn {
                     pr = mk_congr1_th(f_types[i-1], f, new_f, arg(e, i), pr);
                 }
             }
-            return rewrite(e, result(out, pr, heq_proof));
+            return rewrite_app(e, result(out, pr, heq_proof));
         }
     }
 
+    result rewrite_app(expr const & e, result const & r) {
+        if (m_beta && is_lambda(arg(r.m_out, 0)))
+            return rewrite(e, result(head_beta_reduce(r.m_out), r.m_proof, r.m_heq_proof));
+        else
+            return rewrite(e, r);
+    }
+
     expr                   m_target;    // temp field
     buffer<optional<expr>> m_subst;     // temp field
     buffer<expr>           m_new_args;  // temp field
@@ -439,6 +460,11 @@ class simplifier_fn {
         return rewrite(e, result(e));
     }
 
+    result rewrite_lambda(expr const & e, result const & r) {
+
+        rewrite(e, r);
+    }
+
     result simplify_lambda(expr const & e) {
         lean_assert(is_lambda(e));
         if (m_has_heq) {
@@ -450,14 +476,14 @@ class simplifier_fn {
             lean_assert(!res_body.m_heq_proof);
             expr new_body = res_body.m_out;
             if (is_eqp(new_body, abst_body(e)))
-                return result(e);
+                return rewrite_lambda(e, result(e));
             expr out = mk_lambda(e, new_body);
             if (!m_proofs_enabled || !res_body.m_proof)
-                return result(out);
+                return rewrite_lambda(e, result(out));
             expr body_type = infer_type(abst_body(e));
             expr pr  = mk_funext_th(abst_domain(e), mk_lambda(e, body_type), e, out,
                                     mk_lambda(e, *res_body.m_proof));
-            return result(out, pr);
+            return rewrite_lambda(e, result(out, pr));
         }
     }
 
@@ -472,15 +498,15 @@ class simplifier_fn {
             lean_assert(!res_body.m_heq_proof);
             expr new_body = res_body.m_out;
             if (is_eqp(new_body, abst_body(e)))
-                return result(e);
+                return rewrite(e, result(e));
             expr out = mk_pi(abst_name(e), abst_domain(e), new_body);
             if (!m_proofs_enabled || !res_body.m_proof)
-                return result(out);
+                return rewrite(e, result(out));
             expr pr  = mk_allext_th(abst_domain(e),
                                     mk_lambda(e, abst_body(e)),
                                     mk_lambda(e, abst_body(out)),
                                     mk_lambda(e, *res_body.m_proof));
-            return result(out, pr);
+            return rewrite(e, result(out, pr));
         } else {
             // if the environment does not contain heq axioms, then we don't simplify Pi's that are not forall's
             return result(e);
@@ -509,6 +535,7 @@ class simplifier_fn {
         m_single_pass    = get_simplifier_single_pass(o);
         m_beta           = get_simplifier_beta(o);
         m_unfold         = get_simplifier_unfold(o);
+        m_conditional    = get_simplifier_conditional(o);
         m_max_steps      = get_simplifier_max_steps(o);
     }
 
diff --git a/tests/lua/simp1.lua b/tests/lua/simp1.lua
index ec1a8fbec..57ce1293b 100644
--- a/tests/lua/simp1.lua
+++ b/tests/lua/simp1.lua
@@ -28,3 +28,9 @@ print(e)
 print(pr)
 local env = get_environment()
 print(env:type_check(pr))
+
+e, pr = simplify(parse_lean('(fun x, f (f x (0 + a)) (g (b + 0))) b'))
+print(e)
+print(pr)
+local env = get_environment()
+print(env:type_check(pr))