diff --git a/src/library/tactic/apply_tactic.cpp b/src/library/tactic/apply_tactic.cpp
index 967bb935a..aed4ad198 100644
--- a/src/library/tactic/apply_tactic.cpp
+++ b/src/library/tactic/apply_tactic.cpp
@@ -185,6 +185,12 @@ proof_state_seq apply_tactic_core(environment const & env, io_state const & ios,
     return apply_tactic_core(env, ios, s, e, tmp_cs, AddDiff, AddSubgoals);
 }
 
+proof_state_seq fapply_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, AddDiff, AddAllSubgoals);
+}
+
 tactic apply_tactic_core(expr const & e, constraint_seq const & cs) {
     return tactic([=](environment const & env, io_state const & ios, proof_state const & s) {
             return apply_tactic_core(env, ios, s, e, cs);
diff --git a/src/library/tactic/apply_tactic.h b/src/library/tactic/apply_tactic.h
index 1c1a4f5d9..7919052c9 100644
--- a/src/library/tactic/apply_tactic.h
+++ b/src/library/tactic/apply_tactic.h
@@ -9,6 +9,7 @@ Author: Leonardo de Moura
 #include "library/tactic/elaborate.h"
 namespace lean {
 proof_state_seq apply_tactic_core(environment const & env, io_state const & ios, proof_state const & s, expr const & e, constraint_seq const & cs);
+proof_state_seq fapply_tactic_core(environment const & env, io_state const & ios, proof_state const & s, expr const & e, constraint_seq const & cs);
 tactic apply_tactic_core(expr const & e, constraint_seq const & cs = constraint_seq());
 tactic apply_tactic(elaborate_fn const & fn, expr const & e);
 tactic fapply_tactic(elaborate_fn const & fn, expr const & e);
diff --git a/src/library/tactic/constructor_tactic.cpp b/src/library/tactic/constructor_tactic.cpp
index 114cfaa25..19e7f4e67 100644
--- a/src/library/tactic/constructor_tactic.cpp
+++ b/src/library/tactic/constructor_tactic.cpp
@@ -83,7 +83,7 @@ tactic constructor_tactic(elaborate_fn const & elab, optional<unsigned> _i, opti
                     return proof_state_seq();
                 }
             }
-            return apply_tactic_core(env, ios, new_s, C, cs);
+            return fapply_tactic_core(env, ios, new_s, C, cs);
         };
 
         if (_i) {
diff --git a/tests/lean/run/676.lean b/tests/lean/run/676.lean
new file mode 100644
index 000000000..136d199d0
--- /dev/null
+++ b/tests/lean/run/676.lean
@@ -0,0 +1,12 @@
+import data.nat
+open nat
+
+inductive foo : Prop :=
+mk : ∀ {a : nat}, a > 0 → foo
+
+example (b : nat) (h : b > 1) : foo :=
+begin
+  constructor,
+  exact b,
+  exact lt_of_succ_lt h
+end
diff --git a/tests/lean/run/soundness.lean b/tests/lean/run/soundness.lean
index 5c33e2d07..e1cd93b95 100644
--- a/tests/lean/run/soundness.lean
+++ b/tests/lean/run/soundness.lean
@@ -90,26 +90,26 @@ namespace PropF
   lemma weakening2 : ∀ {Γ A Δ}, Γ ⊢ A → Γ ⊆ Δ → Δ ⊢ A
   | Γ ⌞A⌟     Δ (Nax Γ A Hin)          Hs := by constructor; exact Hs Hin
   | Γ ⌞A ⇒ B⌟ Δ (ImpI Γ A B H)         Hs := by constructor; exact weakening2 H (cons_sub_cons A Hs)
-  | Γ ⌞B⌟     Δ (ImpE Γ A B H₁ H₂)     Hs := by constructor; exact weakening2 H₁ Hs; exact weakening2 H₂ Hs
+  | Γ ⌞B⌟     Δ (ImpE Γ A B H₁ H₂)     Hs := by constructor; eassumption; exact weakening2 H₁ Hs; exact weakening2 H₂ Hs
   | Γ ⌞A⌟     Δ (BotC Γ A H)           Hs := by constructor; exact weakening2 H (cons_sub_cons (~A) Hs)
   | Γ ⌞A ∧ B⌟ Δ (AndI Γ A B H₁ H₂)     Hs := by constructor; exact weakening2 H₁ Hs; exact weakening2 H₂ Hs
-  | Γ ⌞A⌟     Δ (AndE₁ Γ A B H)        Hs := by constructor; exact weakening2 H Hs
-  | Γ ⌞B⌟     Δ (AndE₂ Γ A B H)        Hs := by constructor; exact weakening2 H Hs
+  | Γ ⌞A⌟     Δ (AndE₁ Γ A B H)        Hs := by constructor; eassumption; exact weakening2 H Hs
+  | Γ ⌞B⌟     Δ (AndE₂ Γ A B H)        Hs := by constructor; eassumption; exact weakening2 H Hs
   | Γ ⌞A ∨ B⌟ Δ (OrI₁ Γ A B H)         Hs := by constructor; exact weakening2 H Hs
   | Γ ⌞A ∨ B⌟ Δ (OrI₂ Γ A B H)         Hs := by constructor; exact weakening2 H Hs
   | Γ ⌞C⌟     Δ (OrE Γ A B C H₁ H₂ H₃) Hs :=
-       by constructor; exact weakening2 H₁ Hs; exact weakening2 H₂ (cons_sub_cons A Hs); exact weakening2 H₃ (cons_sub_cons B Hs)
+       by constructor; eassumption; eassumption; exact weakening2 H₁ Hs; exact weakening2 H₂ (cons_sub_cons A Hs); exact weakening2 H₃ (cons_sub_cons B Hs)
 
   lemma weakening : ∀ Γ Δ A, Γ ⊢ A → Γ++Δ ⊢ A :=
   λ Γ Δ A H, weakening2 H (sub_append_left Γ Δ)
 
   lemma deduction : ∀ Γ A B, Γ ⊢ A ⇒ B → A::Γ ⊢ B :=
-  λ Γ A B H, by constructor; exact weakening2 H (sub_cons A Γ); constructor; exact mem_cons A Γ
+  λ Γ A B H, by constructor; exact A; exact weakening2 H (sub_cons A Γ); constructor; exact mem_cons A Γ
 
   lemma prov_impl : ∀ A B, Provable (A ⇒ B) → ∀ Γ, Γ ⊢ A → Γ ⊢ B :=
   λ A B Hp Γ Ha,
     assert wHp : Γ ⊢ (A ⇒ B), from !weakening Hp,
-    by constructor; eassumption; eassumption
+    by constructor; eassumption; eassumption; eassumption
 
   lemma Satisfies_cons : ∀ {A Γ v}, Satisfies v Γ → is_true (TrueQ v A) → Satisfies v (A::Γ) :=
   λ A Γ v s t B BinAG,