diff --git a/hott/algebra/field.hlean b/hott/algebra/field.hlean
index 298aeb1122..67b8250119 100644
--- a/hott/algebra/field.hlean
+++ b/hott/algebra/field.hlean
@@ -115,7 +115,7 @@ section division_ring
     symm (eq_one_div_of_mul_eq_one this)
 
   theorem division_ring.one_div_neg_eq_neg_one_div (H : a ≠ 0) : 1 / (- a) = - (1 / a) :=
-    have -1 ≠ 0, from
+    have -1 ≠ (0:A), from
       (suppose -1 = 0, absurd (symm (calc
           1 = -(-1) : neg_neg
         ... = -0    : this
diff --git a/hott/init/funext.hlean b/hott/init/funext.hlean
index e030ceb286..92905c4c46 100644
--- a/hott/init/funext.hlean
+++ b/hott/init/funext.hlean
@@ -181,15 +181,14 @@ section
   theorem nondep_funext_from_ua {A : Type} {B : Type}
       : Π {f g : A → B}, f ~ g → f = g :=
     (λ (f g : A → B) (p : f ~ g),
-        let d := λ (x : A), sigma.mk (f x , f x) idp in
-        let e := λ (x : A), sigma.mk (f x , g x) (p x) in
-        let precomp1 :=  compose (pr₁ ∘ pr1) in
-        have equiv1 [visible] : is_equiv precomp1,
+        let d := λ (x : A), @sigma.mk (B × B) (λ (xy : B × B), xy.1 = xy.2) (f x , f x) (eq.refl (f x, f x).1) in
+        let e := λ (x : A), @sigma.mk (B × B) (λ (xy : B × B), xy.1 = xy.2) (f x , g x) (p x) in
+        let precomp1 :=  compose (pr₁ ∘ sigma.pr1) in
+        assert equiv1 : is_equiv precomp1,
           from @isequiv_src_compose A B,
-        have equiv2 [visible] : Π x y, is_equiv (ap precomp1),
+        assert equiv2 : Π (x y : A → diagonal B), is_equiv (ap precomp1),
           from is_equiv.is_equiv_ap precomp1,
-        have H' : Π (x y : A → diagonal B),
-            pr₁ ∘ pr1 ∘ x = pr₁ ∘ pr1 ∘ y → x = y,
+        have H' : Π (x y : A → diagonal B), pr₁ ∘ pr1 ∘ x = pr₁ ∘ pr1 ∘ y → x = y,
           from (λ x y, is_equiv.inv (ap precomp1)),
         have eq2 : pr₁ ∘ pr1 ∘ d = pr₁ ∘ pr1 ∘ e,
           from idp,
diff --git a/hott/types/pi.hlean b/hott/types/pi.hlean
index 3d960f5d7b..32affc0866 100644
--- a/hott/types/pi.hlean
+++ b/hott/types/pi.hlean
@@ -301,8 +301,8 @@ namespace pi
   theorem is_hprop_pi_eq [instance] [priority 490] (a : A) : is_hprop (Π(a' : A), a = a') :=
   is_hprop_of_imp_is_contr
   ( assume (f : Πa', a = a'),
-    assert H : is_contr A, from is_contr.mk a f,
-    _)
+    assert is_contr A, from is_contr.mk a f,
+    by exact _) /- force type clas resolution -/
 
   theorem is_hprop_neg (A : Type) : is_hprop (¬A) := _
   local attribute ne [reducible]
diff --git a/tests/lean/extra/bag.lean b/tests/lean/extra/bag.lean
index 7ed165ae7b..72a7dec3a3 100644
--- a/tests/lean/extra/bag.lean
+++ b/tests/lean/extra/bag.lean
@@ -291,7 +291,7 @@ private lemma max_count_eq (l₁ l₂ : list A) : ∀ {a : A} {l : list A}, a 
 | a (b::l) h₁ h₂ :=
   assert nodup l, from nodup_of_nodup_cons h₂,
   assert b ∉ l,   from not_mem_of_nodup_cons h₂,
-  or.elim h₁
+  or.elim (eq_or_mem_of_mem_cons h₁)
   (suppose a = b,
     have a ∉ l, by rewrite this; assumption,
     assert a ∉ max_count l₁ l₂ l, from not_mem_max_count_of_not_mem l₁ l₂ this,
@@ -337,7 +337,7 @@ private lemma min_count_eq (l₁ l₂ : list A) : ∀ {a : A} {l : list A}, a 
 | a (b::l) h₁ h₂ :=
   assert nodup l, from nodup_of_nodup_cons h₂,
   assert b ∉ l,   from not_mem_of_nodup_cons h₂,
-  or.elim h₁
+  or.elim (eq_or_mem_of_mem_cons h₁)
   (suppose a = b,
     have a ∉ l, by rewrite this; assumption,
     assert a ∉ min_count l₁ l₂ l, from not_mem_min_count_of_not_mem l₁ l₂ this,
diff --git a/tests/lean/finset_induction_bug.lean.expected.out b/tests/lean/finset_induction_bug.lean.expected.out
index 53e651aa68..21ad4e10f9 100644
--- a/tests/lean/finset_induction_bug.lean.expected.out
+++ b/tests/lean/finset_induction_bug.lean.expected.out
@@ -19,7 +19,9 @@ u : nodup_list A,
 l : list A,
 a : A,
 l' : list A,
-IH : ∀ (x : @nodup A l'), P (@quot.mk (nodup_list A) (nodup_list_setoid A) (@subtype.tag (list A) (@nodup A) l' x)),
+IH :
+  ∀ (has_property : @nodup A l'),
+    P (@quot.mk (nodup_list A) (nodup_list_setoid A) (@subtype.tag (list A) (@nodup A) l' has_property)),
 nodup_al' : @nodup A (@cons A a l'),
 anl' : not (@list.mem A a l'),
 H3 : @eq (list A) (@list.insert A (λ (a b : A), h a b) a l') (@cons A a l'),
@@ -41,7 +43,9 @@ u : nodup_list A,
 l : list A,
 a : A,
 l' : list A,
-IH : ∀ (x : @nodup A l'), P (@quot.mk (nodup_list A) (nodup_list_setoid A) (@subtype.tag (list A) (@nodup A) l' x)),
+IH :
+  ∀ (has_property : @nodup A l'),
+    P (@quot.mk (nodup_list A) (nodup_list_setoid A) (@subtype.tag (list A) (@nodup A) l' has_property)),
 nodup_al' : @nodup A (@cons A a l'),
 anl' : not (@list.mem A a l'),
 H3 : @eq (list A) (@list.insert A (λ (a b : A), h a b) a l') (@cons A a l'),
diff --git a/tests/lean/run/class8.lean b/tests/lean/run/class8.lean
index 47d9d8320a..70efc9c92c 100644
--- a/tests/lean/run/class8.lean
+++ b/tests/lean/run/class8.lean
@@ -30,7 +30,7 @@ set_option trace.class_instances true
 theorem T1 {A B C D : Type} {P : C → Prop} (a : A) (H1 : inh B) (H2 : ∃x, P x) : inh ((A → A) × B × (D → C) × Prop) :=
 have h1 [visible] : inh A, from inh.intro a,
 have h2 [visible] : inh C, from inh_exists H2,
-_
+by exact _
 
 reveal T1
 (*
diff --git a/tests/lean/run/trans.lean b/tests/lean/run/trans.lean
index be1a6d3777..9d782e6d25 100644
--- a/tests/lean/run/trans.lean
+++ b/tests/lean/run/trans.lean
@@ -23,10 +23,3 @@ theorem dcongr {A : Type} {B : A → Type} {a b : A} (f : Π x, B x) (p : a = b)
 := have H1 : ∀ p1 : a = a, transport p1 (f a) = f a, from
      assume p1 : a = a, transport_eq p1 (f a),
    eq.rec H1 p p
-
-theorem transport_trans {A : Type} {a b c : A} {P : A → Type} (p1 : a = b) (p2 : b = c) (H : P a) :
-                       transport p1 (transport p2 H) = transport (trans p1 p2) H
-:= have H1 : ∀ p, transport p1 (transport p H) = transport (trans p1 p) H, from
-     take p, calc transport p1 (transport p H) = transport p1 H           : {transport_eq p H}
-                                          ...  = transport (trans p1 p) H : refl (transport p1 H),
-   eq.rec H1 p2 p2