diff --git a/src/library/tactic/smt/congruence_closure.cpp b/src/library/tactic/smt/congruence_closure.cpp
index eba0afa376..77f3d76eff 100644
--- a/src/library/tactic/smt/congruence_closure.cpp
+++ b/src/library/tactic/smt/congruence_closure.cpp
@@ -500,6 +500,8 @@ void congruence_closure::apply_simple_eqvs(expr const & e) {
     expr const & fn = get_app_fn(e);
     if (is_lambda(fn)) {
         expr reduced_e = head_beta_reduce(e);
+        if (m_phandler)
+            m_phandler->new_aux_cc_term(reduced_e);
         internalize_core(reduced_e, none_expr());
         push_refl_eq(e, reduced_e);
     }
diff --git a/src/library/tactic/smt/congruence_closure.h b/src/library/tactic/smt/congruence_closure.h
index 91490bf98f..a146ea52b2 100644
--- a/src/library/tactic/smt/congruence_closure.h
+++ b/src/library/tactic/smt/congruence_closure.h
@@ -25,6 +25,9 @@ public:
     virtual ~cc_propagation_handler() {}
     virtual void propagated(unsigned n, expr const * data) = 0;
     void propagated(buffer<expr> const & p) { propagated(p.size(), p.data()); }
+    /* Congruence closure module invokes the following method when
+       a new auxiliary term is created during propagation. */
+    virtual void new_aux_cc_term(expr const & e) = 0;
 };
 
 /* The congruence_closure module (optionally) uses a normalizer.
diff --git a/src/library/tactic/smt/ematch.cpp b/src/library/tactic/smt/ematch.cpp
index 8f82236223..06a2159e08 100644
--- a/src/library/tactic/smt/ematch.cpp
+++ b/src/library/tactic/smt/ematch.cpp
@@ -688,6 +688,16 @@ struct ematch_fn {
         return true;
     }
 
+    bool match_args_prefix(state & s, buffer<expr> const & p_args, expr const & t) {
+        unsigned t_nargs = get_app_num_args(t);
+        expr it = t;
+        while (t_nargs > p_args.size()) {
+            t_nargs--;
+            it = app_fn(it);
+        }
+        return match_args(s, p_args, it);
+    }
+
     bool process_continue(expr const & p) {
         lean_trace(name({"debug", "ematch"}), tout() << "process_continue: " << p << "\n";);
         buffer<expr> p_args;
@@ -697,7 +707,7 @@ struct ematch_fn {
             s->for_each([&](expr const & t) {
                     if (m_cc.is_congr_root(t) || m_cc.in_heterogeneous_eqc(t)) {
                         state new_state = m_state;
-                        if (match_args(new_state, p_args, t))
+                        if (match_args_prefix(new_state, p_args, t))
                             new_states.push_back(new_state);
                     }
                 });
@@ -919,7 +929,7 @@ struct ematch_fn {
         expr const & fn = get_app_args(p, p_args);
         if (!m_ctx.is_def_eq(fn, get_app_fn(t)))
             return;
-        if (!match_args(m_state, p_args, t))
+        if (!match_args_prefix(m_state, p_args, t))
             return;
         search(lemma);
     }
diff --git a/src/library/tactic/smt/smt_state.cpp b/src/library/tactic/smt/smt_state.cpp
index 3c2ed72d3d..938fadb6ee 100644
--- a/src/library/tactic/smt/smt_state.cpp
+++ b/src/library/tactic/smt/smt_state.cpp
@@ -88,6 +88,10 @@ void smt::internalize(expr const & e) {
     m_goal.m_em_state.internalize(m_ctx, e);
 }
 
+void smt::new_aux_cc_term(expr const & e) {
+    m_goal.m_em_state.internalize(m_ctx, e);
+}
+
 void smt::add(expr const & type, expr const & proof) {
     m_goal.m_em_state.internalize(m_ctx, type);
     m_cc.add(type, proof);
diff --git a/src/library/tactic/smt/smt_state.h b/src/library/tactic/smt/smt_state.h
index 6d17f10a34..c95505d4b7 100644
--- a/src/library/tactic/smt/smt_state.h
+++ b/src/library/tactic/smt/smt_state.h
@@ -52,6 +52,7 @@ private:
     lbool get_value_core(expr const & e);
     lbool get_value(expr const & e);
     virtual void propagated(unsigned n, expr const * p) override;
+    virtual void new_aux_cc_term(expr const & e) override;
     virtual expr normalize(expr const & e) override;
 public:
     smt(type_context & ctx, defeq_can_state & dcs, smt_goal & g);
diff --git a/tests/lean/run/ematch_partial_apps.lean b/tests/lean/run/ematch_partial_apps.lean
new file mode 100644
index 0000000000..20ba2cb7ea
--- /dev/null
+++ b/tests/lean/run/ematch_partial_apps.lean
@@ -0,0 +1,42 @@
+open tactic
+
+meta def check_expr (p : pexpr) (t : expr) : tactic unit :=
+do e ← to_expr p, guard (expr.alpha_eqv t e)
+
+meta def check_target (p : pexpr) : tactic unit :=
+do t ← target, check_expr p t
+
+set_option trace.smt.ematch true
+
+example (a : list nat) (f : nat → nat) : a = [1, 2] → a^.for f = [f 1, f 2] :=
+begin [smt]
+  intros,
+  ematch_using [list.for],
+  ematch_using [flip],
+  ematch_using [list.map],
+  ematch_using [list.map],
+  ematch_using [list.map]
+end
+
+example (a : list nat) (f : nat → nat) : a = [1, 2] → a^.for f = [f 1, f 2] :=
+begin [smt]
+  intros,
+  repeat {ematch_using [list.for, flip, list.map], try { close }},
+end
+
+attribute [ematch] list.map flip list.for
+
+example (a : list nat) (f : nat → nat) : a = [1, 2] → a^.for f = [f 1, f 2] :=
+begin [smt]
+  intros, eblast
+end
+
+constant f : nat → nat → nat
+constant g : nat → nat → nat
+axiom fgx : ∀ x y, (: f x :) = (λ y, y) ∧ (: g y :) = λ x, 0
+attribute [ematch] fgx
+
+example (a b c : nat) : f a b = b ∧ g b c = 0 :=
+begin [smt]
+  ematch
+end