diff --git a/src/library/blast/unit/unit_propagate.cpp b/src/library/blast/unit/unit_propagate.cpp
index fd8065dbab..befe4cdaa1 100644
--- a/src/library/blast/unit/unit_propagate.cpp
+++ b/src/library/blast/unit/unit_propagate.cpp
@@ -9,6 +9,7 @@ Author: Daniel Selsam
 #include "library/constants.h"
 #include "library/util.h"
 #include "library/blast/blast.h"
+#include "library/blast/trace.h"
 #include "library/blast/action_result.h"
 #include "library/blast/unit/unit_actions.h"
 #include "library/blast/proof_expr.h"
@@ -20,8 +21,7 @@ Author: Daniel Selsam
 
 namespace lean {
 namespace blast {
-
-bool is_lemma(expr const & _type) {
+static bool is_lemma(expr const & _type) {
     expr type = _type;
     bool has_antecedent = false;
     if (!is_prop(type)) return false;
@@ -34,11 +34,20 @@ bool is_lemma(expr const & _type) {
     else return false;
 }
 
-bool is_fact(expr const & type) {
-    return !is_lemma(type);
+/** \brief We say \c type is a dependent lemma iff
+    - \c type is a proposition
+    - \c type is of the form (Pi (x : A), B)
+    - 'A' is a proposition
+    - 'B' depends on 'x' */
+static bool is_dep_lemma(expr const & type) {
+    return is_pi(type) && is_prop(type) && is_prop(binding_domain(type)) && !closed(binding_body(type));
 }
 
-expr flip(expr const & e) {
+static bool is_fact(expr const & type) {
+    return !is_lemma(type) && !is_dep_lemma(type);
+}
+
+static expr flip(expr const & e) {
     expr not_e;
     if (!blast::is_not(e, not_e)) {
         // we use whnf to make sure we get a uniform representation
@@ -53,12 +62,15 @@ struct unit_branch_extension : public branch_extension {
     /* We map each lemma to the two facts that it is watching. */
     rb_multi_map<hypothesis_idx, expr, unsigned_cmp> m_lemmas_to_facts;
 
-    /* We map each fact back to the lemma hypotheses that are watching it. */
+    /* We map each fact (i.e., the type of the hypothesis) back to the lemma hypotheses that are watching it. */
     rb_multi_map<expr, hypothesis_idx, expr_quick_cmp> m_facts_to_lemmas;
 
-    /* We map each fact expression to its hypothesis. */
+    /* We map each fact expression (i.e., the type of the hypothesis) to its hypothesis. */
     rb_map<expr, hypothesis_idx, expr_quick_cmp>       m_facts;
 
+    /* We map each fact (i.e., the type of the hypothesis) back to the dependent lemma hypotheses that are watching it. */
+    rb_multi_map<expr, hypothesis_idx, expr_quick_cmp> m_facts_to_dep_lemmas;
+
     unit_branch_extension() {}
     unit_branch_extension(unit_branch_extension const & b):
         m_lemmas_to_facts(b.m_lemmas_to_facts),
@@ -77,9 +89,16 @@ struct unit_branch_extension : public branch_extension {
                         unwatch(hidx, fact);
                     });
             }
+        } else if (is_dep_lemma(h.get_type())) {
+            expr fact_type = binding_domain(h.get_type());
+            m_facts_to_lemmas.erase(fact_type, hidx);
         } else if (is_fact(h.get_type())) {
             m_facts.erase(h.get_type());
+            // TODO(Leo): it is not clear to me why the following assertion should hold.
+            // I think we need
+            //     m_facts_to_lemmas.erase(h.get_type())
             lean_assert(!find_lemmas_watching_fact(h.get_type()));
+            m_facts_to_dep_lemmas.erase(h.get_type());
         }
     }
 
@@ -103,6 +122,9 @@ public:
         m_lemmas_to_facts.insert(lemma_hidx, fact_type);
         m_facts_to_lemmas.insert(fact_type, lemma_hidx);
     }
+    list<hypothesis_idx> const * find_dep_lemmas_watching_fact(expr const & fact_type) {
+        return m_facts_to_dep_lemmas.find(fact_type);
+    }
 };
 
 void initialize_unit_propagate() {
@@ -136,7 +158,7 @@ static unit_branch_extension & get_extension() {
 */
 
 
-bool can_propagate(expr const & _type, buffer<expr, 2> & to_watch) {
+static bool can_propagate(expr const & _type, buffer<expr, 2> & to_watch) {
     lean_assert(is_lemma(_type));
     expr type = _type;
     unsigned num_watching = 0;
@@ -178,7 +200,7 @@ bool can_propagate(expr const & _type, buffer<expr, 2> & to_watch) {
     return !missing_non_Prop;
 }
 
-action_result unit_lemma(hypothesis_idx hidx, expr const & _type, expr const & _proof) {
+static action_result unit_lemma(hypothesis_idx hidx, expr const & _type, expr const & _proof) {
     lean_assert(is_lemma(_type));
     unit_branch_extension & ext = get_extension();
 
@@ -270,16 +292,51 @@ action_result unit_lemma(hypothesis_idx hidx, expr const & _type, expr const & _
     return action_result::new_branch();
 }
 
-action_result unit_fact(expr const & type) {
+static action_result unit_dep_lemma(hypothesis_idx hidx, expr type, expr proof) {
+    lean_assert(is_dep_lemma(type));
+    unit_branch_extension & ext = get_extension();
+    bool propagated = false;
+    while (is_pi(type)) {
+        expr d = binding_domain(type);
+        if (auto hidx = ext.find_fact(d)) {
+            propagated = true;
+            expr h     = mk_href(*hidx);
+            proof      = mk_app(proof, h);
+            type       = instantiate(binding_body(type), h);
+        } else {
+            break;
+        }
+    }
+    if (propagated) {
+        curr_state().del_hypothesis(hidx);
+        curr_state().mk_hypothesis(type, proof);
+        return action_result::new_branch();
+    }
+    lean_assert(is_pi(type));
+    ext.m_facts_to_dep_lemmas.insert(binding_domain(type), hidx);
+    return action_result::failed();
+}
+
+static action_result unit_fact(expr const & type) {
     unit_branch_extension & ext = get_extension();
-    list<hypothesis_idx> const * lemmas = ext.find_lemmas_watching_fact(type);
-    if (!lemmas) return action_result::failed();
     bool success = false;
-    for_each(*lemmas, [&](hypothesis_idx const & hidx) {
-            hypothesis const & h = curr_state().get_hypothesis_decl(hidx);
-            action_result r = unit_lemma(hidx, whnf(h.get_type()), h.get_self());
-            success = success || (r.get_kind() == action_result::NewBranch);
-        });
+    /* non dependent lemmas */
+    if (list<hypothesis_idx> const * lemmas = ext.find_lemmas_watching_fact(type)) {
+        for_each(*lemmas, [&](hypothesis_idx const & hidx) {
+                hypothesis const & h = curr_state().get_hypothesis_decl(hidx);
+                // TODO(Leo): it is not clear to me why we need whnf in the following statement.
+                action_result r = unit_lemma(hidx, whnf(h.get_type()), h.get_self());
+                success = success || (r.get_kind() == action_result::NewBranch);
+            });
+    }
+    /* dependent lemmas */
+    if (list<hypothesis_idx> const * lemmas = ext.find_dep_lemmas_watching_fact(type)) {
+        for_each(*lemmas, [&](hypothesis_idx const & hidx) {
+                hypothesis const & h = curr_state().get_hypothesis_decl(hidx);
+                action_result r = unit_dep_lemma(hidx, whnf(h.get_type()), h.get_self());
+                success = success || (r.get_kind() == action_result::NewBranch);
+            });
+    }
     if (success) return action_result::new_branch();
     else return action_result::failed();
 }
@@ -288,6 +345,7 @@ action_result unit_propagate(unsigned hidx) {
     hypothesis const & h = curr_state().get_hypothesis_decl(hidx);
     expr type = whnf(h.get_type());
     if (is_lemma(type)) return unit_lemma(hidx, type, h.get_self());
+    else if (is_dep_lemma(type)) return unit_dep_lemma(hidx, type, h.get_self());
     else if (is_fact(type)) return unit_fact(type);
     else return action_result::failed();
 }
diff --git a/tests/lean/run/blast_unit_dep.lean b/tests/lean/run/blast_unit_dep.lean
new file mode 100644
index 0000000000..9a4f323015
--- /dev/null
+++ b/tests/lean/run/blast_unit_dep.lean
@@ -0,0 +1,22 @@
+constant p : nat → Prop
+constant q : Π a, p a → Prop
+
+set_option blast.strategy "unit"
+
+example (a : nat) (h₁ : p a) (h₂ : ∀ h : p a, q a h) : q a h₁ :=
+by blast
+
+example (a : nat) (h₂ : ∀ h : p a, q a h) (h₁ : p a) : q a h₁ :=
+by blast
+
+example (a b : nat) (H : ∀ (p₁ : p a) (p₂ : p b), q b p₂ → q a p₁) (h₁ : p a) (h₂ : p b) : q b h₂ → q a h₁ :=
+by blast
+
+example (a b : nat) (h₂ : p b) (H : ∀ (p₁ : p a) (p₂ : p b), q b p₂ → q a p₁) (h₁ : p a) : q b h₂ → q a h₁ :=
+by blast
+
+example (a b : nat) (h₂ : p b) (h₁ : p a) (H : ∀ (p₁ : p a) (p₂ : p b), q b p₂ → q a p₁) : q b h₂ → q a h₁ :=
+by blast
+
+example (a b : nat) (h₁ : p a) (H : ∀ (p₁ : p a) (p₂ : p b), q b p₂ → q a p₁) (h₂ : p b) : q b h₂ → q a h₁ :=
+by blast