diff --git a/library/data/list/basic.lean b/library/data/list/basic.lean
index 057ba99eb..d9c1dc480 100644
--- a/library/data/list/basic.lean
+++ b/library/data/list/basic.lean
@@ -418,10 +418,10 @@ definition has_decidable_eq {A : Type} [H : decidable_eq A] : ∀ l₁ l₂ : li
   match H a b with
   | inl Hab  :=
     match has_decidable_eq l₁ l₂ with
-    | inl He := inl (eq.rec_on Hab (eq.rec_on He rfl))
-    | inr Hn := inr (λ H, list.no_confusion H (λ Hab Ht, absurd Ht Hn))
+    | inl He := inl (by congruence; repeat assumption)
+    | inr Hn := inr (by intro H; injection H; contradiction)
     end
-  | inr Hnab := inr (λ H, list.no_confusion H (λ Hab Ht, absurd Hab Hnab))
+  | inr Hnab := inr (by intro H; injection H; contradiction)
   end
 
 /- quasiequal a l l' means that l' is exactly l, with a added
diff --git a/library/data/num.lean b/library/data/num.lean
index 758d95c8b..98bb11655 100644
--- a/library/data/num.lean
+++ b/library/data/num.lean
@@ -64,16 +64,16 @@ namespace pos_num
   | (bit0 a) one      := inr (by contradiction)
   | (bit0 a) (bit0 b) :=
     match decidable_eq a b with
-    | inl H₁  := inl (eq.rec_on H₁ rfl)
-    | inr H₁  := inr (λ H, pos_num.no_confusion H (λ H₂, absurd H₂ H₁))
+    | inl H₁  := inl (by rewrite H₁)
+    | inr H₁  := inr (by intro H; injection H; contradiction)
     end
   | (bit0 a) (bit1 b) := inr (by contradiction)
   | (bit1 a) one      := inr (by contradiction)
   | (bit1 a) (bit0 b) := inr (by contradiction)
   | (bit1 a) (bit1 b) :=
     match decidable_eq a b with
-    | inl H₁  := inl (eq.rec_on H₁ rfl)
-    | inr H₁  := inr (λ H, pos_num.no_confusion H (λ H₂, absurd H₂ H₁))
+    | inl H₁  := inl (by rewrite H₁)
+    | inr H₁  := inr (by intro H; injection H; contradiction)
     end
 
   local notation a < b         := (lt a b = tt)
diff --git a/library/data/option.lean b/library/data/option.lean
index bf15efd78..ada56bb09 100644
--- a/library/data/option.lean
+++ b/library/data/option.lean
@@ -34,6 +34,6 @@ namespace option
   | (some v₁) (some v₂) :=
     match H v₁ v₂ with
     | inl e := by left; congruence; assumption
-    | inr n := by right; intro h; injection h; refine absurd _ n; assumption
+    | inr n := by right; intro h; injection h; contradiction
     end
 end option
diff --git a/library/data/prod.lean b/library/data/prod.lean
index 1e0198029..a1369da43 100644
--- a/library/data/prod.lean
+++ b/library/data/prod.lean
@@ -24,9 +24,9 @@ namespace prod
     | inl e₁ :=
       match h₂ b b' with
       | inl e₂ := by left; congruence; repeat assumption
-      | inr n₂ := by right; intro h; injection h; refine absurd _ n₂; assumption
+      | inr n₂ := by right; intro h; injection h; contradiction
       end
-    | inr n₁ := by right; intro h; injection h; refine absurd _ n₁; assumption
+    | inr n₁ := by right; intro h; injection h; contradiction
     end
 
   definition swap {A : Type} : A × A → A × A
diff --git a/library/data/string.lean b/library/data/string.lean
index 5efce9b5a..c5eed5186 100644
--- a/library/data/string.lean
+++ b/library/data/string.lean
@@ -28,7 +28,7 @@ begin
   apply (@by_cases (a₇ = b₇)), intros,
   apply (@by_cases (a₈ = b₈)), intros,
   left, congruence, repeat assumption,
-  repeat (intro n; right; intro h; injection h; refine absurd _ n; assumption)
+  repeat (intro n; right; intro h; injection h; contradiction)
 end
 
 open string
@@ -42,7 +42,7 @@ definition decidable_eq_string [instance] : ∀ s₁ s₂ : string, decidable (s
   | inl e₁ :=
     match decidable_eq_string r₁ r₂ with
     | inl e₂ := by left; congruence; repeat assumption
-    | inr n₂ := by right; intro h; injection h; refine absurd _ n₂; assumption
+    | inr n₂ := by right; intro h; injection h; contradiction
     end
-  | inr n₁ := by right; intro h; injection h; refine absurd _ n₁; assumption
+  | inr n₁ := by right; intro h; injection h; contradiction
   end
diff --git a/library/data/subtype.lean b/library/data/subtype.lean
index 6aa894fb4..39508d099 100644
--- a/library/data/subtype.lean
+++ b/library/data/subtype.lean
@@ -33,6 +33,6 @@ namespace subtype
     begin
       apply (@by_cases (v₁ = v₂)),
         {intro e, revert p₁, rewrite e, intro p₁, left, congruence},
-        {intro n, right, intro h, injection h, refine absurd _ n, assumption}
+        {intro n, right, intro h, injection h, contradiction}
     end
 end subtype
diff --git a/library/data/sum.lean b/library/data/sum.lean
index 10d3d9948..570d428d3 100644
--- a/library/data/sum.lean
+++ b/library/data/sum.lean
@@ -41,13 +41,13 @@ namespace sum
   | has_decidable_eq (inl a₁) (inl a₂) :=
     match h₁ a₁ a₂ with
       | decidable.inl hp := by left; congruence; assumption
-      | decidable.inr hn := by right; intro h; injection h; refine absurd _ hn; assumption
+      | decidable.inr hn := by right; intro h; injection h; contradiction
     end
   | has_decidable_eq (inl a₁) (inr b₂) := by right; contradiction
   | has_decidable_eq (inr b₁) (inl a₂) := by right; contradiction
   | has_decidable_eq (inr b₁) (inr b₂) :=
     match h₂ b₁ b₂ with
       | decidable.inl hp := by left; congruence; assumption
-      | decidable.inr hn := by right; intro h; injection h; refine absurd _ hn; assumption
+      | decidable.inr hn := by right; intro h; injection h; contradiction
     end
 end sum
diff --git a/library/data/vector.lean b/library/data/vector.lean
index a46e90e0c..04e3f4db0 100644
--- a/library/data/vector.lean
+++ b/library/data/vector.lean
@@ -263,8 +263,8 @@ namespace vector
     | inl Hab  :=
       match decidable_eq v₁ v₂ with
       | inl He := by left; congruence; repeat assumption
-      | inr Hn := by right; intro h; injection h; refine absurd _ Hn; assumption
+      | inr Hn := by right; intro h; injection h; contradiction
       end
-    | inr Hnab := by right; intro h; injection h; refine absurd _ Hnab; assumption
+    | inr Hnab := by right; intro h; injection h; contradiction
   end
 end vector
diff --git a/library/init/nat.lean b/library/init/nat.lean
index 7914bf340..53fdee935 100644
--- a/library/init/nat.lean
+++ b/library/init/nat.lean
@@ -35,7 +35,7 @@ namespace nat
   | has_decidable_eq (succ x) (succ y) :=
       match has_decidable_eq x y with
       | inl xeqy := inl (by rewrite xeqy)
-      | inr xney := inr (λ h : succ x = succ y, by injection h with xeqy; exact absurd xeqy xney)
+      | inr xney := inr (by intro h; injection h; contradiction)
       end
 
   -- less-than is well-founded