diff --git a/library/data/int/basic.lean b/library/data/int/basic.lean
index ee9651a15..1ac2bcf84 100644
--- a/library/data/int/basic.lean
+++ b/library/data/int/basic.lean
@@ -528,7 +528,7 @@ begin
     {rewrite add.comm4}
 end
 
-protected theorem mul_right_distrib (a b c : ℤ) : (a + b) * c = a * c + b * c :=
+protected theorem right_distrib (a b c : ℤ) : (a + b) * c = a * c + b * c :=
 eq_of_repr_equiv_repr
   (calc
     repr ((a + b) * c) = pmul (repr (a + b)) (repr c) : repr_mul
@@ -538,10 +538,10 @@ eq_of_repr_equiv_repr
       ... = padd (repr (a * c)) (repr (b * c))                     : repr_mul
       ... ≡ repr (a * c + b * c)                                   : repr_add)
 
-protected theorem mul_left_distrib (a b c : ℤ) : a * (b + c) = a * b + a * c :=
+protected theorem left_distrib (a b c : ℤ) : a * (b + c) = a * b + a * c :=
 calc
   a * (b + c) = (b + c) * a : int.mul_comm
-    ... = b * a + c * a : int.mul_right_distrib
+    ... = b * a + c * a : int.right_distrib
     ... = a * b + c * a : int.mul_comm
     ... = a * b + a * c : int.mul_comm
 
@@ -567,8 +567,8 @@ protected definition integral_domain [reducible] [trans_instance] : algebra.inte
   one            := 1,
   one_mul        := int.one_mul,
   mul_one        := int.mul_one,
-  left_distrib   := int.mul_left_distrib,
-  right_distrib  := int.mul_right_distrib,
+  left_distrib   := int.left_distrib,
+  right_distrib  := int.right_distrib,
   mul_comm       := int.mul_comm,
   zero_ne_one    := int.zero_ne_one,
   eq_zero_or_eq_zero_of_mul_eq_zero := @int.eq_zero_or_eq_zero_of_mul_eq_zero⦄
diff --git a/library/data/int/div.lean b/library/data/int/div.lean
index 6246ff994..32f6c9d17 100644
--- a/library/data/int/div.lean
+++ b/library/data/int/div.lean
@@ -406,7 +406,7 @@ calc
   a * b div (a * c) = a * (b div c * c + b mod c) div (a * c) : eq_div_mul_add_mod
 
     ... = (a * (b mod c) + a * c * (b div c)) div (a * c)     :
-              by rewrite [!add.comm, int.mul_left_distrib, mul.comm _ c, -!mul.assoc]
+              by rewrite [!add.comm, int.left_distrib, mul.comm _ c, -!mul.assoc]
     ... = a * (b mod c) div (a * c) + b div c                 : !int.add_mul_div_self_left H3
     ... = 0 + b div c                                         : {!div_eq_zero_of_lt H5 H4}
     ... = b div c                                             : zero_add
diff --git a/tests/lean/interactive/findp.input.expected.out b/tests/lean/interactive/findp.input.expected.out
index f8f4c4b86..00573eb46 100644
--- a/tests/lean/interactive/findp.input.expected.out
+++ b/tests/lean/interactive/findp.input.expected.out
@@ -9,7 +9,6 @@ false.rec_on|Π (C : Type), false → C
 false.cases_on|Π (C : Type), false → C
 false.induction_on|∀ (C : Prop), false → C
 true_ne_false|¬true = false
-nat.lt_self_iff_false|∀ (n : ℕ), n < n ↔ false
 not_of_is_false|is_false ?c → ¬?c
 not_of_iff_false|(?a ↔ false) → ¬?a
 is_false|Π (c : Prop) [H : decidable c], Prop
diff --git a/tests/lean/run/div2.lean b/tests/lean/run/div2.lean
index f5c9005d0..703a58906 100644
--- a/tests/lean/run/div2.lean
+++ b/tests/lean/run/div2.lean
@@ -78,8 +78,8 @@ nat.case_strong_induction_on m
             take z,
               assume Hzx : measure z < measure x,
               calc
-                f' m z = restrict default measure f m z : IH m !le.refl z
-                  ... = f z : !restrict_lt_eq (lt_of_lt_of_le Hzx (le_of_lt_succ H1))
+                f' m z = restrict default measure f m z : IH m !nat.le_refl z
+                  ... = f z : !restrict_lt_eq (nat.lt_of_lt_of_le Hzx (le_of_lt_succ H1))
           ∎,
           have H2 : f' (succ m) x = rec_val x f,
           proof
diff --git a/tests/lean/run/div_wf.lean b/tests/lean/run/div_wf.lean
index 9c4f45ccc..154e5ad58 100644
--- a/tests/lean/run/div_wf.lean
+++ b/tests/lean/run/div_wf.lean
@@ -4,7 +4,7 @@ open nat well_founded decidable prod eq.ops
 -- Auxiliary lemma used to justify recursive call
 private definition lt_aux {x y : nat} (H : 0 < y ∧ y ≤ x) : x - y < x :=
 and.rec_on H (λ ypos ylex,
-  sub_lt (lt_of_lt_of_le ypos ylex) ypos)
+  sub_lt (nat.lt_of_lt_of_le ypos ylex) ypos)
 
 definition wdiv.F (x : nat) (f : Π x₁, x₁ < x → nat → nat) (y : nat) : nat :=
 if H : 0 < y ∧ y ≤ x then f (x - y) (lt_aux H) y + 1 else zero
diff --git a/tests/lean/run/eq17.lean b/tests/lean/run/eq17.lean
index c704120dc..1dd742a9f 100644
--- a/tests/lean/run/eq17.lean
+++ b/tests/lean/run/eq17.lean
@@ -1,5 +1,5 @@
 open nat
 
 definition lt_of_succ : ∀ {a b : nat}, succ a < b → a < b
-| lt_of_succ (lt.base (succ a)) := lt.trans (lt.base a) (lt.base (succ a))
+| lt_of_succ (lt.base (succ a)) := nat.lt_trans (lt.base a) (lt.base (succ a))
 | lt_of_succ (lt.step h)        := lt.step  (lt_of_succ h)
diff --git a/tests/lean/run/fib_wrec.lean b/tests/lean/run/fib_wrec.lean
index dd6e6c78f..faebd4c84 100644
--- a/tests/lean/run/fib_wrec.lean
+++ b/tests/lean/run/fib_wrec.lean
@@ -8,7 +8,7 @@ nat.cases_on n
     (λ (f : Π (m : nat), m < (succ zero) → nat), succ zero)
     (λ (n₂ : nat) (f : Π (m : nat), m < (succ (succ n₂)) → nat),
        have l₁ : succ n₂ < succ (succ n₂), from lt.base (succ n₂),
-       have l₂ : n₂ < succ (succ n₂), from lt.trans (lt.base n₂) l₁,
+       have l₂ : n₂ < succ (succ n₂), from nat.lt_trans (lt.base n₂) l₁,
          f (succ n₂) l₁ + f n₂ l₂))
 
 definition fib (n : nat) :=
diff --git a/tests/lean/run/nested_rec.lean b/tests/lean/run/nested_rec.lean
index 950127fb4..a248e4fb8 100644
--- a/tests/lean/run/nested_rec.lean
+++ b/tests/lean/run/nested_rec.lean
@@ -5,13 +5,13 @@ open nat prod sigma
 --   g (succ x) := g (g x)
 definition g.F (x : nat) : (Π y, y < x → Σ r : nat, r ≤ y) → Σ r : nat, r ≤ x :=
 nat.cases_on x
-  (λ f, ⟨zero, le.refl zero⟩)
+  (λ f, ⟨zero, nat.le_refl zero⟩)
   (λ x₁ (f : Π y, y < succ x₁ → Σ r : nat, r ≤ y),
      let p₁    := f x₁ (lt.base x₁) in
      let gx₁   := pr₁ p₁ in
-     let p₂    := f gx₁ (lt_of_le_of_lt (pr₂ p₁) (lt.base x₁)) in
+     let p₂    := f gx₁ (nat.lt_of_le_of_lt (pr₂ p₁) (lt.base x₁)) in
      let ggx₁  := pr₁ p₂ in
-     ⟨ggx₁, le_succ_of_le (le.trans (pr₂ p₂) (pr₂ p₁))⟩)
+     ⟨ggx₁, le_succ_of_le (nat.le_trans (pr₂ p₂) (pr₂ p₁))⟩)
 
 definition g (x : nat) : nat :=
 pr₁ (well_founded.fix g.F x)
diff --git a/tests/lean/run/rewriter6.lean b/tests/lean/run/rewriter6.lean
index 75c3277d6..1490ff6d7 100644
--- a/tests/lean/run/rewriter6.lean
+++ b/tests/lean/run/rewriter6.lean
@@ -10,4 +10,4 @@ by rewrite ^sub -- unfold sub
 definition double (x : int) := x + x
 
 theorem double_zero (x : int) : double (0 + x) = (1 + 1)*x :=
-by rewrite [↑double, zero_add, mul.right_distrib, one_mul]
+by rewrite [↑double, int.zero_add, int.right_distrib, int.one_mul]
diff --git a/tests/lean/run/tree_height.lean b/tests/lean/run/tree_height.lean
index 1a4976950..18f4be207 100644
--- a/tests/lean/run/tree_height.lean
+++ b/tests/lean/run/tree_height.lean
@@ -25,7 +25,7 @@ theorem height_lt.node_right {A : Type} (t₁ t₂ : tree A) : height_lt t₂ (n
 lt_succ_of_le (le_max_right (height t₁) (height t₂))
 
 theorem height_lt.trans {A : Type} : transitive (@height_lt A) :=
-inv_image.trans lt height @lt.trans
+inv_image.trans lt height @nat.lt_trans
 
 example : height_lt (leaf (2:nat)) (node (leaf 1) (leaf 2)) :=
 !height_lt.node_right
diff --git a/tests/lean/rw_set2.lean.expected.out b/tests/lean/rw_set2.lean.expected.out
index 288702e14..4f688c884 100644
--- a/tests/lean/rw_set2.lean.expected.out
+++ b/tests/lean/rw_set2.lean.expected.out
@@ -7,7 +7,6 @@ simplification rules for iff
 #2, ?M_1 - ?M_2 < succ ?M_1 ↦ true
 #1, ?M_1 < 0 ↦ false
 #1, ?M_1 < succ ?M_1 ↦ true
-#1, ?M_1 < ?M_1 ↦ false
 #1, 0 < succ ?M_1 ↦ true
 simplification rules for eq
 #1, g ?M_1 ↦ f ?M_1 + 1