diff --git a/hott/algebra/category/functor.hlean b/hott/algebra/category/functor.hlean
index f0069c9f8a..968b098afb 100644
--- a/hott/algebra/category/functor.hlean
+++ b/hott/algebra/category/functor.hlean
@@ -204,7 +204,7 @@ namespace functor
     (q : (λ(a b : C) (f : hom a b), hom_of_eq (p b) ∘ F₁ f ∘ inv_of_eq (p a)) ∼3 to_fun_hom F₂) (c : C) :
     ap010 to_fun_ob (functor_eq p q) c = p c :=
   begin
-    cases F₂, revert q, apply (homotopy.rec_on p), clear p, esimp, intro p q,
+    cases F₂, revert q, eapply (homotopy.rec_on p), clear p, esimp, intro p q,
     apply sorry,
     --apply (homotopy3.rec_on q), clear q, intro q,
     --cases p, --TODO: report: this fails
diff --git a/hott/init/tactic.hlean b/hott/init/tactic.hlean
index d0778a4a8d..33f6708f47 100644
--- a/hott/init/tactic.hlean
+++ b/hott/init/tactic.hlean
@@ -67,6 +67,7 @@ definition identifier_list := expr_list
 definition opt_identifier_list := expr_list
 
 opaque definition apply      (e : expr)            : tactic := builtin
+opaque definition eapply     (e : expr)            : tactic := builtin
 opaque definition fapply     (e : expr)            : tactic := builtin
 opaque definition rename     (a b : identifier)    : tactic := builtin
 opaque definition intro      (e : identifier_list) : tactic := builtin
diff --git a/hott/types/hprop_trunc.hlean b/hott/types/hprop_trunc.hlean
index 07ca4ec310..392a00338b 100644
--- a/hott/types/hprop_trunc.hlean
+++ b/hott/types/hprop_trunc.hlean
@@ -40,7 +40,7 @@ namespace is_trunc
   definition is_hprop_is_trunc [instance] (n : trunc_index) :
     Π (A : Type), is_hprop (is_trunc n A) :=
   begin
-    apply (trunc_index.rec_on n),
+    eapply (trunc_index.rec_on n),
     { intro A,
       apply is_trunc_is_equiv_closed,
       { apply equiv.to_is_equiv, apply is_contr.sigma_char},
diff --git a/hott/types/pi.hlean b/hott/types/pi.hlean
index e429380f86..b42e3f395c 100644
--- a/hott/types/pi.hlean
+++ b/hott/types/pi.hlean
@@ -158,7 +158,7 @@ namespace pi
       [H : ∀a, is_trunc n (B a)] : is_trunc n (Πa, B a) :=
   begin
     revert B H,
-    apply (trunc_index.rec_on n),
+    eapply (trunc_index.rec_on n),
       {intro B H,
         fapply is_contr.mk,
           intro a, apply center,
diff --git a/hott/types/sigma.hlean b/hott/types/sigma.hlean
index 11c3ab7160..6491854237 100644
--- a/hott/types/sigma.hlean
+++ b/hott/types/sigma.hlean
@@ -365,7 +365,7 @@ namespace sigma
       [HA : is_trunc n A] [HB : Πa, is_trunc n (B a)] : is_trunc n (Σa, B a) :=
   begin
   revert A B HA HB,
-  apply (trunc_index.rec_on n),
+  eapply (trunc_index.rec_on n),
     intro A B HA HB,
       fapply is_trunc.is_trunc_equiv_closed,
         apply equiv.symm,
diff --git a/hott/types/trunc.hlean b/hott/types/trunc.hlean
index a59d7dba30..5453554b2b 100644
--- a/hott/types/trunc.hlean
+++ b/hott/types/trunc.hlean
@@ -58,7 +58,7 @@ namespace is_trunc
     (n : trunc_index) [HA : is_trunc n A] : is_trunc n B :=
   begin
     revert A B f Hf HA,
-    apply (trunc_index.rec_on n),
+    eapply (trunc_index.rec_on n),
     { clear n, intro A B f Hf HA, cases Hf with g ε, fapply is_contr.mk,
       { exact f (center A)},
       { intro b, apply concat,
@@ -154,7 +154,7 @@ namespace trunc
     fapply equiv.MK,
     { intro p, cases p, apply (trunc.rec_on aa),
       intro a, esimp [trunc_eq_type,trunc.rec_on], exact (tr idp)},
-    { apply (trunc.rec_on aa'), apply (trunc.rec_on aa),
+    { eapply (trunc.rec_on aa'), eapply (trunc.rec_on aa),
       intro a a' x, esimp [trunc_eq_type, trunc.rec_on] at x,
       apply (trunc.rec_on x), intro p, exact (ap tr p)},
     {
@@ -173,14 +173,14 @@ namespace trunc
   definition is_trunc_trunc_of_is_trunc [instance] [priority 500] (A : Type)
     (n m : trunc_index) [H : is_trunc n A] : is_trunc n (trunc m A) :=
   begin
-    revert A m H, apply (trunc_index.rec_on n),
+    revert A m H, eapply (trunc_index.rec_on n),
     { clear n, intro A m H, apply is_contr_equiv_closed,
       { apply equiv_trunc, apply (@is_trunc_of_leq _ -2), exact unit.star} },
     { clear n, intro n IH A m H, cases m with m,
       { apply (@is_trunc_of_leq _ -2), exact unit.star},
       { apply is_trunc_succ_intro, intro aa aa',
         apply (@trunc.rec_on _ _ _ aa  (λy, !is_trunc_succ_of_is_hprop)),
-        apply (@trunc.rec_on _ _ _ aa' (λy, !is_trunc_succ_of_is_hprop)),
+        eapply (@trunc.rec_on _ _ _ aa' (λy, !is_trunc_succ_of_is_hprop)),
         intro a a', apply (is_trunc_equiv_closed_rev),
         { apply tr_eq_tr_equiv},
         { exact (IH _ _ _)}}}
diff --git a/library/data/fintype.lean b/library/data/fintype.lean
index 851d0acf2c..4cee0a434f 100644
--- a/library/data/fintype.lean
+++ b/library/data/fintype.lean
@@ -181,7 +181,7 @@ private theorem mem_ltype_elems {A : Type} {s : list A} {a : ⟪s⟫}
    begin
       revert vaeqb h,
       -- TODO(Leo): check why 'cases a with va, ma' produces an incorrect proof
-      apply as_type.cases_on a,
+      eapply as_type.cases_on a,
       intro va ma vaeqb,
       rewrite -vaeqb, intro h,
       apply mem_cons
diff --git a/library/data/list/comb.lean b/library/data/list/comb.lean
index 0ece60a887..c535d17ee5 100644
--- a/library/data/list/comb.lean
+++ b/library/data/list/comb.lean
@@ -259,7 +259,7 @@ theorem zip_unzip : ∀ (l : list (A × B)), zip (pr₁ (unzip l)) (pr₂ (unzip
     rewrite unzip_cons,
     have r : zip (pr₁ (unzip l)) (pr₂ (unzip l)) = l, from zip_unzip l,
     revert r,
-    apply prod.cases_on (unzip l),
+    eapply prod.cases_on (unzip l),
     intro la lb r,
     rewrite -r
   end
diff --git a/library/data/list/perm.lean b/library/data/list/perm.lean
index e3cbcf247d..0cbfb095bc 100644
--- a/library/data/list/perm.lean
+++ b/library/data/list/perm.lean
@@ -138,7 +138,7 @@ assume p, gen [a] p rfl
 theorem eq_singlenton_of_perm (a b : A) : [a] ~ [b] → a = b :=
 assume p,
 begin
-  injection eq_singlenton_of_perm_inv a p with e₁ e₂,
+  injection eq_singlenton_of_perm_inv a p with e₁,
   rewrite e₁
 end
 
diff --git a/library/init/tactic.lean b/library/init/tactic.lean
index 7c127bcc10..88c8654f64 100644
--- a/library/init/tactic.lean
+++ b/library/init/tactic.lean
@@ -67,6 +67,7 @@ definition identifier_list := expr_list
 definition opt_identifier_list := expr_list
 
 opaque definition apply      (e : expr)         : tactic := builtin
+opaque definition eapply     (e : expr)         : tactic := builtin
 opaque definition fapply     (e : expr)         : tactic := builtin
 opaque definition rename     (a b : identifier) : tactic := builtin
 opaque definition intro      (e : identifier_list) : tactic := builtin
diff --git a/src/emacs/lean-syntax.el b/src/emacs/lean-syntax.el
index 24f4bcf355..3733535d48 100644
--- a/src/emacs/lean-syntax.el
+++ b/src/emacs/lean-syntax.el
@@ -132,7 +132,7 @@
      (,(rx (not (any "\.")) word-start
            (group
             (or "\\b.*_tac" "Cond" "or_else" "then" "try" "when" "assumption" "eassumption" "rapply"
-                "apply" "fapply" "rename" "intro" "intros" "all_goals" "fold"
+                "apply" "fapply" "eapply" "rename" "intro" "intros" "all_goals" "fold"
                 "generalize" "generalizes" "clear" "clears" "revert" "reverts" "back" "beta" "done" "exact" "rexact"
                 "refine" "repeat" "whnf" "rotate" "rotate_left" "rotate_right" "inversion" "cases" "rewrite" "esimp"
                 "unfold" "change" "check_expr" "contradiction" "exfalso" "split" "existsi" "constructor" "left" "right"
diff --git a/src/library/constants.cpp b/src/library/constants.cpp
index 95aa578b63..73d7c45f7f 100644
--- a/src/library/constants.cpp
+++ b/src/library/constants.cpp
@@ -68,6 +68,7 @@ name const * g_tactic = nullptr;
 name const * g_tactic_all_goals = nullptr;
 name const * g_tactic_apply = nullptr;
 name const * g_tactic_assert_hypothesis = nullptr;
+name const * g_tactic_eapply = nullptr;
 name const * g_tactic_fapply = nullptr;
 name const * g_tactic_eassumption = nullptr;
 name const * g_tactic_and_then = nullptr;
@@ -193,6 +194,7 @@ void initialize_constants() {
     g_tactic_all_goals = new name{"tactic", "all_goals"};
     g_tactic_apply = new name{"tactic", "apply"};
     g_tactic_assert_hypothesis = new name{"tactic", "assert_hypothesis"};
+    g_tactic_eapply = new name{"tactic", "eapply"};
     g_tactic_fapply = new name{"tactic", "fapply"};
     g_tactic_eassumption = new name{"tactic", "eassumption"};
     g_tactic_and_then = new name{"tactic", "and_then"};
@@ -319,6 +321,7 @@ void finalize_constants() {
     delete g_tactic_all_goals;
     delete g_tactic_apply;
     delete g_tactic_assert_hypothesis;
+    delete g_tactic_eapply;
     delete g_tactic_fapply;
     delete g_tactic_eassumption;
     delete g_tactic_and_then;
@@ -444,6 +447,7 @@ name const & get_tactic_name() { return *g_tactic; }
 name const & get_tactic_all_goals_name() { return *g_tactic_all_goals; }
 name const & get_tactic_apply_name() { return *g_tactic_apply; }
 name const & get_tactic_assert_hypothesis_name() { return *g_tactic_assert_hypothesis; }
+name const & get_tactic_eapply_name() { return *g_tactic_eapply; }
 name const & get_tactic_fapply_name() { return *g_tactic_fapply; }
 name const & get_tactic_eassumption_name() { return *g_tactic_eassumption; }
 name const & get_tactic_and_then_name() { return *g_tactic_and_then; }
diff --git a/src/library/constants.h b/src/library/constants.h
index 2d2a63eecf..15e3ff4f0d 100644
--- a/src/library/constants.h
+++ b/src/library/constants.h
@@ -70,6 +70,7 @@ name const & get_tactic_name();
 name const & get_tactic_all_goals_name();
 name const & get_tactic_apply_name();
 name const & get_tactic_assert_hypothesis_name();
+name const & get_tactic_eapply_name();
 name const & get_tactic_fapply_name();
 name const & get_tactic_eassumption_name();
 name const & get_tactic_and_then_name();
diff --git a/src/library/constants.txt b/src/library/constants.txt
index 04ee7a80ff..26959c81d7 100644
--- a/src/library/constants.txt
+++ b/src/library/constants.txt
@@ -63,6 +63,7 @@ tactic
 tactic.all_goals
 tactic.apply
 tactic.assert_hypothesis
+tactic.eapply
 tactic.fapply
 tactic.eassumption
 tactic.and_then
diff --git a/src/library/tactic/apply_tactic.cpp b/src/library/tactic/apply_tactic.cpp
index feb509b3ef..1c9826f386 100644
--- a/src/library/tactic/apply_tactic.cpp
+++ b/src/library/tactic/apply_tactic.cpp
@@ -67,9 +67,11 @@ static void remove_redundant_metas(buffer<expr> & metas) {
 
 enum subgoals_action_kind { IgnoreSubgoals, AddRevSubgoals, AddSubgoals, AddAllSubgoals };
 
+enum add_meta_kind { DoNotAdd, AddDiff, AddAll };
+
 static proof_state_seq apply_tactic_core(environment const & env, io_state const & ios, proof_state const & s,
                                          expr const & _e, buffer<constraint> & cs,
-                                         bool add_meta, subgoals_action_kind subgoals_action) {
+                                         add_meta_kind add_meta, subgoals_action_kind subgoals_action) {
     goals const & gs = s.get_goals();
     if (empty(gs)) {
         throw_no_goal_if_enabled(s);
@@ -90,12 +92,17 @@ static proof_state_seq apply_tactic_core(environment const & env, io_state const
     local_context ctx;
     bool initialized_ctx = false;
     unifier_config cfg(ios.get_options());
-    if (add_meta) {
-        // unsigned num_t   = get_expect_num_args(*tc, t);
+    if (add_meta != DoNotAdd) {
         unsigned num_e_t = get_expect_num_args(*tc, e_t);
-        // Remark: we used to add (num_e_t - num_t) arguments.
-        // This would allow us to handle (A -> B) without using intros,
-        // but it was preventing us from solving other problems
+        if (add_meta == AddDiff) {
+            unsigned num_t   = get_expect_num_args(*tc, t);
+            if (num_t <= num_e_t)
+                num_e_t -= num_t;
+            else
+                num_e_t = 0;
+        } else {
+            lean_assert(add_meta == AddAll);
+        }
         for (unsigned i = 0; i < num_e_t; i++) {
             auto e_t_cs = tc->whnf(e_t);
             e_t_cs.second.linearize(cs);
@@ -171,7 +178,7 @@ static proof_state_seq apply_tactic_core(environment const & env, io_state const
 }
 
 static proof_state_seq apply_tactic_core(environment const & env, io_state const & ios, proof_state const & s, expr const & e,
-                                         bool add_meta, subgoals_action_kind subgoals_action) {
+                                         add_meta_kind add_meta, subgoals_action_kind subgoals_action) {
     buffer<constraint> cs;
     return apply_tactic_core(env, ios, s, e, cs, add_meta, subgoals_action);
 }
@@ -179,7 +186,7 @@ static proof_state_seq apply_tactic_core(environment const & env, io_state const
 proof_state_seq apply_tactic_core(environment const & env, io_state const & ios, proof_state const & s, expr const & e, constraint_seq const & cs) {
     buffer<constraint> tmp_cs;
     cs.linearize(tmp_cs);
-    return apply_tactic_core(env, ios, s, e, tmp_cs, true, AddSubgoals);
+    return apply_tactic_core(env, ios, s, e, tmp_cs, AddDiff, AddSubgoals);
 }
 
 tactic apply_tactic_core(expr const & e, constraint_seq const & cs) {
@@ -201,13 +208,13 @@ tactic eassumption_tactic() {
             buffer<expr> hs;
             get_app_args(g.get_meta(), hs);
             for (expr const & h : hs) {
-                r = append(r, apply_tactic_core(env, ios, new_s, h, false, IgnoreSubgoals));
+                r = append(r, apply_tactic_core(env, ios, new_s, h, DoNotAdd, IgnoreSubgoals));
             }
             return r;
         });
 }
 
-tactic apply_tactic_core(elaborate_fn const & elab, expr const & e, subgoals_action_kind k) {
+tactic apply_tactic_core(elaborate_fn const & elab, expr const & e, add_meta_kind add_meta, subgoals_action_kind k) {
     return tactic([=](environment const & env, io_state const & ios, proof_state const & s) {
             goals const & gs = s.get_goals();
             if (empty(gs)) {
@@ -223,16 +230,20 @@ tactic apply_tactic_core(elaborate_fn const & elab, expr const & e, subgoals_act
             to_buffer(ecs.second, cs);
             to_buffer(s.get_postponed(), cs);
             proof_state new_s(s, ngen, constraints());
-            return apply_tactic_core(env, ios, new_s, new_e, cs, true, k);
+            return apply_tactic_core(env, ios, new_s, new_e, cs, add_meta, k);
         });
 }
 
 tactic apply_tactic(elaborate_fn const & elab, expr const & e) {
-    return apply_tactic_core(elab, e, AddSubgoals);
+    return apply_tactic_core(elab, e, AddDiff, AddSubgoals);
 }
 
 tactic fapply_tactic(elaborate_fn const & elab, expr const & e) {
-    return apply_tactic_core(elab, e, AddAllSubgoals);
+    return apply_tactic_core(elab, e, AddDiff, AddAllSubgoals);
+}
+
+tactic eapply_tactic(elaborate_fn const & elab, expr const & e) {
+    return apply_tactic_core(elab, e, AddAll, AddSubgoals);
 }
 
 int mk_eassumption_tactic(lua_State * L) { return push_tactic(L, eassumption_tactic()); }
@@ -252,6 +263,12 @@ void initialize_apply_tactic() {
                      return apply_tactic(fn, get_tactic_expr_expr(app_arg(e)));
                  });
 
+    register_tac(get_tactic_eapply_name(),
+                 [](type_checker &, elaborate_fn const & fn, expr const & e, pos_info_provider const *) {
+                     check_tactic_expr(app_arg(e), "invalid 'eapply' tactic, invalid argument");
+                     return eapply_tactic(fn, get_tactic_expr_expr(app_arg(e)));
+                 });
+
     register_tac(get_tactic_fapply_name(),
                  [](type_checker &, elaborate_fn const & fn, expr const & e, pos_info_provider const *) {
                      check_tactic_expr(app_arg(e), "invalid 'fapply' tactic, invalid argument");
diff --git a/tests/lean/hott/get_tac1.hlean b/tests/lean/hott/get_tac1.hlean
index b404277e95..28a621fd83 100644
--- a/tests/lean/hott/get_tac1.hlean
+++ b/tests/lean/hott/get_tac1.hlean
@@ -3,7 +3,7 @@ open eq
 definition concat_pV_p {A : Type} {x y z : A} (p : x = z) (q : y = z) : (p ⬝ q⁻¹) ⬝ q = p :=
 begin
   generalize p,
-  apply (eq.rec_on q),
+  eapply (eq.rec_on q),
   intro p,
   apply (eq.rec_on p),
   apply idp
diff --git a/tests/lean/run/361.lean b/tests/lean/run/361.lean
new file mode 100644
index 0000000000..6c09a76704
--- /dev/null
+++ b/tests/lean/run/361.lean
@@ -0,0 +1,6 @@
+variables {P Q R : Prop}
+theorem foo (H : P → Q → R) (x : P) : Q → R :=
+begin
+  apply H,
+  exact x
+end
diff --git a/tests/lean/run/revert_tac.lean b/tests/lean/run/revert_tac.lean
index 47e6336d81..1f86509f7c 100644
--- a/tests/lean/run/revert_tac.lean
+++ b/tests/lean/run/revert_tac.lean
@@ -12,7 +12,7 @@ theorem foo1 {A : Type} (a b c : A) (P : A → Prop) : P a → a = b → P b :=
 begin
   intros [Hp, Heq],
   revert Hp,
-  apply (eq.rec_on Heq),
+  eapply (eq.rec_on Heq),
   intro Hpa,
   apply Hpa
 end
diff --git a/tests/lean/run/reverts_tac.lean b/tests/lean/run/reverts_tac.lean
index 9b3e0a34ab..a0eaf0dd66 100644
--- a/tests/lean/run/reverts_tac.lean
+++ b/tests/lean/run/reverts_tac.lean
@@ -13,7 +13,7 @@ begin
   intros  [Hp, Heq],
   reverts [Heq, Hp],
   intro Heq,
-  apply (eq.rec_on Heq),
+  eapply (eq.rec_on Heq),
   intro Pa,
   apply Pa
 end