diff --git a/library/algebra/category/functor.lean b/library/algebra/category/functor.lean
index 97dc6bc01..580f18ae8 100644
--- a/library/algebra/category/functor.lean
+++ b/library/algebra/category/functor.lean
@@ -6,7 +6,7 @@ Module: algebra.category.functor
 Author: Floris van Doorn
 -/
 import .basic
-import logic.cast logic.funext
+import logic.cast algebra.function
 open function
 open category eq eq.ops heq
 
diff --git a/library/algebra/function.lean b/library/algebra/function.lean
index 11a8eacde..c7ef29668 100644
--- a/library/algebra/function.lean
+++ b/library/algebra/function.lean
@@ -7,6 +7,8 @@ Author: Leonardo de Moura
 
 General operations on functions.
 -/
+import logic.cast
+
 namespace function
 
 variables {A : Type} {B : Type} {C : Type} {D : Type} {E : Type}
@@ -95,6 +97,23 @@ have h : f a = b, from calc
    ... = id b         : by rewrite (right_inv_eq inv)
    ... = b            : rfl,
 exists.intro a h
+
+  theorem compose.assoc (f : C → D) (g : B → C) (h : A → B) : (f ∘ g) ∘ h = f ∘ (g ∘ h) :=
+  funext (take x, rfl)
+
+  theorem compose.left_id (f : A → B) : id ∘ f = f :=
+  funext (take x, rfl)
+
+  theorem compose.right_id (f : A → B) : f ∘ id = f :=
+  funext (take x, rfl)
+
+  theorem compose_const_right (f : B → C) (b : B) : f ∘ (const A b) = const A (f b) :=
+  funext (take x, rfl)
+
+  theorem hfunext {A : Type} {B : A → Type} {B' : A → Type} {f : Π x, B x} {g : Π x, B' x}
+                  (H : ∀ a, f a == g a) : f == g :=
+  let HH : B = B' := (funext (λ x, heq.type_eq (H x))) in
+    cast_to_heq (funext (λ a, heq.to_eq (heq.trans (cast_app HH f a) (H a))))
 end function
 
 -- copy reducible annotations to top-level
diff --git a/library/logic/funext.lean b/library/logic/funext.lean
deleted file mode 100644
index ba2771261..000000000
--- a/library/logic/funext.lean
+++ /dev/null
@@ -1,31 +0,0 @@
-/-
-Copyright (c) 2015 Microsoft Corporation. All rights reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-
-Author: Leonardo de Moura
-
-Basic theorems for functions
--/
-import logic.cast algebra.function data.sigma
-open function eq.ops
-
-namespace function
-  variables {A B C D: Type}
-
-  theorem compose.assoc (f : C → D) (g : B → C) (h : A → B) : (f ∘ g) ∘ h = f ∘ (g ∘ h) :=
-  funext (take x, rfl)
-
-  theorem compose.left_id (f : A → B) : id ∘ f = f :=
-  funext (take x, rfl)
-
-  theorem compose.right_id (f : A → B) : f ∘ id = f :=
-  funext (take x, rfl)
-
-  theorem compose_const_right (f : B → C) (b : B) : f ∘ (const A b) = const A (f b) :=
-  funext (take x, rfl)
-
-  theorem hfunext {A : Type} {B : A → Type} {B' : A → Type} {f : Π x, B x} {g : Π x, B' x}
-                  (H : ∀ a, f a == g a) : f == g :=
-  let HH : B = B' := (funext (λ x, heq.type_eq (H x))) in
-    cast_to_heq (funext (λ a, heq.to_eq (heq.trans (cast_app HH f a) (H a))))
-end function
diff --git a/tests/lean/550.lean b/tests/lean/550.lean
index 23db6e7da..d0f159231 100644
--- a/tests/lean/550.lean
+++ b/tests/lean/550.lean
@@ -1,5 +1,4 @@
 import algebra.function
-import logic.funext
 
 open function
 
diff --git a/tests/lean/550.lean.expected.out b/tests/lean/550.lean.expected.out
index fb5d33b39..3c90a002a 100644
--- a/tests/lean/550.lean.expected.out
+++ b/tests/lean/550.lean.expected.out
@@ -1,4 +1,4 @@
-550.lean:44:72: error:invalid 'rewrite' tactic, step produced type incorrect term, details: type mismatch at application
+550.lean:43:72: error:invalid 'rewrite' tactic, step produced type incorrect term, details: type mismatch at application
   eq.symm linv
 term
   linv
@@ -27,14 +27,14 @@ rinv : func ∘ finv = function.id
              (eq.symm rinv))
           (eq.symm (function.compose.assoc finv func finv)))
        (function.compose.assoc (finv ∘ func) finv func)) = id
-550.lean:44:47: error: don't know how to synthesize placeholder
+550.lean:43:47: error: don't know how to synthesize placeholder
 A : Type,
 f : bijection A,
 func finv : A → A,
 linv : finv ∘ func = function.id,
 rinv : func ∘ finv = function.id
 ⊢ inv (mk func finv linv rinv) ∘b mk func finv linv rinv = id
-550.lean:44:2: error: failed to add declaration 'bijection.inv.linv' to environment, value has metavariables
+550.lean:43:2: error: failed to add declaration 'bijection.inv.linv' to environment, value has metavariables
 remark: set 'formatter.hide_full_terms' to false to see the complete term
   λ (A : Type) (f : …),
     bijection.rec_on f (λ (func finv : …) (linv : …) (rinv : …), ?M_1)
diff --git a/tests/lean/run/585.lean b/tests/lean/run/585.lean
index 73f33362e..0513887db 100644
--- a/tests/lean/run/585.lean
+++ b/tests/lean/run/585.lean
@@ -6,5 +6,5 @@ check ∅                 -- o.k.
 check λs t, subset s t  -- o.k.
 check λs t, s ⊆ t       -- fixed
 
-infix `⊆`:50 := subset
+infix `⊆` := subset
 check λs t, s ⊆ t
diff --git a/tests/lean/subset_error.lean b/tests/lean/subset_error.lean
index 5736e9c36..8a2f91908 100644
--- a/tests/lean/subset_error.lean
+++ b/tests/lean/subset_error.lean
@@ -12,8 +12,8 @@ definition set.subset {A : Type₁} (s₁ s₂ : set A) : Prop :=
 definition finset.subset {A : Type₁} (s₁ s₂ : finset A) : Prop :=
 ∀ ⦃a : A⦄, a ∈ s₁ → a ∈ s₂
 
-infix `⊆`:50 := set.subset
-infix `⊆`:50 := finset.subset
+infix `⊆` := set.subset
+infix `⊆` := finset.subset
 
 example (A : Type₁) (x : A) (S H : set A) (Pin : x ∈ S) (Psub : S ⊆ H) : x ∈ H :=
 Psub Pin -- Error, we cannot infer at preprocessing time the binder information for Psub
diff --git a/tests/lean/tactic_id_bug.lean b/tests/lean/tactic_id_bug.lean
index a32786a22..24180186c 100644
--- a/tests/lean/tactic_id_bug.lean
+++ b/tests/lean/tactic_id_bug.lean
@@ -1,5 +1,4 @@
 import algebra.function
-import logic.funext
 
 open function
 
diff --git a/tests/lean/tactic_id_bug.lean.expected.out b/tests/lean/tactic_id_bug.lean.expected.out
index 9b6c574d8..b6f349eb3 100644
--- a/tests/lean/tactic_id_bug.lean.expected.out
+++ b/tests/lean/tactic_id_bug.lean.expected.out
@@ -1,4 +1,4 @@
-tactic_id_bug.lean:23:4: proof state
+tactic_id_bug.lean:22:4: proof state
 A : Type,
 gfunc gfinv : A → A,
 glinv : gfinv ∘ gfunc = id,