diff --git a/src/library/blast/simplifier/simplifier.cpp b/src/library/blast/simplifier/simplifier.cpp
index 87e00357b..ec3f5d75f 100644
--- a/src/library/blast/simplifier/simplifier.cpp
+++ b/src/library/blast/simplifier/simplifier.cpp
@@ -168,10 +168,13 @@ class simplifier {
 
     typedef std::unordered_map<key, result, key_hash_fn, key_eq_fn> simplify_cache;
     simplify_cache m_cache;
-
     optional<result> cache_lookup(expr const & e);
     void cache_save(expr const & e, result const & r);
 
+    /* Mapping from subsingleton type to representative */
+    expr_map<expr> m_subsingleton_elem_map;
+    optional<result> normalize_subsingleton_args(expr const & e);
+
     /* Basic helpers */
     bool using_eq() { return m_rel == get_eq_name(); }
 
@@ -370,7 +373,8 @@ expr simplifier::whnf_eta(expr const & e) {
 
 result simplifier::simplify(expr const & e, simp_lemmas const & srss) {
     flet<simp_lemmas> set_srss(m_srss, srss);
-    freset<simplify_cache> reset(m_cache);
+    freset<simplify_cache> reset1(m_cache);
+    freset<expr_map<expr>> reset2(m_subsingleton_elem_map);
     return simplify(e, true);
 }
 
@@ -458,7 +462,22 @@ result simplifier::simplify_lambda(expr const & e) {
         t = instantiate(binding_body(t), l);
     }
 
-    result r = simplify(t, false);
+    result r        = simplify(t, false);
+    expr new_t      = r.get_new();
+    /* check if subsingleton, and normalize */
+    expr new_t_type = m_tmp_tctx->infer(new_t);
+    if (m_tmp_tctx->mk_subsingleton_instance(new_t_type)) {
+        auto it = m_subsingleton_elem_map.find(new_t_type);
+        if (it != m_subsingleton_elem_map.end()) {
+            if (it->second != new_t) {
+                expr proof = get_app_builder().mk_app(get_subsingleton_elim_name(), new_t, it->second);
+                r = join(r, result(it->second, proof));
+            }
+        } else {
+            m_subsingleton_elem_map.insert(mk_pair(new_t_type, new_t));
+        }
+    }
+
     for (int i = ls.size() - 1; i >= 0; --i) r = funext(r, ls[i]);
     return r;
 }
@@ -797,6 +816,61 @@ bool simplifier::instantiate_emetas(blast_tmp_type_context & tmp_tctx, unsigned
     return !failed;
 }
 
+/* Given a function application \c e, replace arguments that are subsingletons with a
+   representative */
+optional<result> simplifier::normalize_subsingleton_args(expr const & e) {
+    buffer<expr> args;
+    get_app_args(e, args);
+    auto congr_lemma = mk_specialized_congr_lemma(e);
+    if (!congr_lemma) return optional<result>();
+    expr proof = congr_lemma->get_proof();
+    expr type = congr_lemma->get_type();
+    unsigned i = 0;
+    bool normalized = false;
+    for_each(congr_lemma->get_arg_kinds(), [&](congr_arg_kind const & ckind) {
+            expr rfl;
+            switch (ckind) {
+            case congr_arg_kind::Fixed:
+                proof = mk_app(proof, args[i]);
+                type = instantiate(binding_body(type), args[i]);
+                break;
+            case congr_arg_kind::FixedNoParam:
+                break;
+            case congr_arg_kind::Eq:
+                proof = mk_app(proof, args[i]);
+                type = instantiate(binding_body(type), args[i]);
+                rfl = get_app_builder().mk_eq_refl(args[i]);
+                proof = mk_app(proof, args[i], rfl);
+                type = instantiate(binding_body(type), args[i]);
+                type = instantiate(binding_body(type), rfl);
+                break;
+            case congr_arg_kind::Cast:
+                proof = mk_app(proof, args[i]);
+                type  = instantiate(binding_body(type), args[i]);
+                expr const & arg_type = binding_domain(type);
+                expr new_arg;
+                auto it = m_subsingleton_elem_map.find(arg_type);
+                if (it != m_subsingleton_elem_map.end()) {
+                    normalized = (it->second != args[i]);
+                    new_arg    = it->second;
+                } else {
+                    new_arg = args[i];
+                    m_subsingleton_elem_map.insert(mk_pair(arg_type, args[i]));
+                }
+                proof = mk_app(proof, new_arg);
+                type = instantiate(binding_body(type), new_arg);
+                break;
+            }
+            i++;
+        });
+    if (!normalized) return optional<result>();
+    lean_assert(is_eq(type));
+    buffer<expr> type_args;
+    get_app_args(type, type_args);
+    expr e_new = type_args[2];
+    return optional<result>(result(e_new, proof));
+}
+
 template<typename F>
 optional<result> simplifier::synth_congr(expr const & e, F && simp) {
     static_assert(std::is_same<typename std::result_of<F(expr const & e)>::type, result>::value,
@@ -843,8 +917,15 @@ optional<result> simplifier::synth_congr(expr const & e, F && simp) {
     buffer<expr> type_args;
     get_app_args(type, type_args);
     expr e_new = remove_unnecessary_casts(type_args[2]);
-    if (has_proof) return optional<result>(result(e_new, proof));
-    else return optional<result>(result(e_new));
+    result r;
+    if (has_proof) r = result(e_new, proof);
+    else r = result(e_new);
+
+    if (has_cast) {
+        if (auto r_norm = normalize_subsingleton_args(e_new))
+            r = join(r, *r_norm);
+    }
+    return optional<result>(r);
 }
 
 expr simplifier::remove_unnecessary_casts(expr const & e) {
diff --git a/tests/lean/run/blast_simp_subsingleton2.lean b/tests/lean/run/blast_simp_subsingleton2.lean
new file mode 100644
index 000000000..f8fd19946
--- /dev/null
+++ b/tests/lean/run/blast_simp_subsingleton2.lean
@@ -0,0 +1,16 @@
+import data.unit
+open nat unit
+
+constant r {A B : Type} : A → B → A
+
+example (a b c d : unit) : r a b = r c d :=
+by simp
+
+example (a b : unit) : a = b :=
+by simp
+
+example (a b : unit) : (λ x : nat, a) = (λ y : nat, b) :=
+by simp
+
+example (a b : unit) : (λ x : nat, r a b) = (λ y : nat, r b b) :=
+by simp