From 9043add656177eeac1491a73d2f3ab92bec0013c Mon Sep 17 00:00:00 2001
From: Benjamin Barenblat <bbaren@debian.org>
Date: Sat, 29 Dec 2018 14:31:27 -0500
Subject: Imported Upstream version 8.8.2

---
 theories/Program/Combinators.v | 22 +++++++++-------------
 1 file changed, 9 insertions(+), 13 deletions(-)

(limited to 'theories/Program/Combinators.v')

diff --git a/theories/Program/Combinators.v b/theories/Program/Combinators.v
index 772018aa..f78d06b1 100644
--- a/theories/Program/Combinators.v
+++ b/theories/Program/Combinators.v
@@ -1,10 +1,12 @@
 (* -*- coding: utf-8 -*- *)
 (************************************************************************)
-(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
-(* <O___,, *   INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016     *)
+(*         *   The Coq Proof Assistant / The Coq Development Team       *)
+(*  v      *   INRIA, CNRS and contributors - Copyright 1999-2018       *)
+(* <O___,, *       (see CREDITS file for the list of authors)           *)
 (*   \VV/  **************************************************************)
-(*    //   *      This file is distributed under the terms of the       *)
-(*         *       GNU Lesser General Public License Version 2.1        *)
+(*    //   *    This file is distributed under the terms of the         *)
+(*         *     GNU Lesser General Public License Version 2.1          *)
+(*         *     (see LICENSE file for the text of the license)         *)
 (************************************************************************)
 (** * Proofs about standard combinators, exports functional extensionality.
 
@@ -22,15 +24,13 @@ Open Scope program_scope.
 Lemma compose_id_left : forall A B (f : A -> B), id ∘ f = f.
 Proof.
   intros.
-  unfold id, compose.
-  symmetry. apply eta_expansion.
+  reflexivity.
 Qed.
 
 Lemma compose_id_right : forall A B (f : A -> B), f ∘ id = f.
 Proof.
   intros.
-  unfold id, compose.
-  symmetry ; apply eta_expansion.
+  reflexivity.
 Qed.
 
 Lemma compose_assoc : forall A B C D (f : A -> B) (g : B -> C) (h : C -> D),
@@ -47,9 +47,7 @@ Hint Rewrite <- @compose_assoc : core.
 
 Lemma flip_flip : forall A B C, @flip A B C ∘ flip = id.
 Proof.
-  unfold flip, compose.
   intros.
-  extensionality x ; extensionality y ; extensionality z.
   reflexivity.
 Qed.
 
@@ -57,9 +55,7 @@ Qed.
 
 Lemma prod_uncurry_curry : forall A B C, @prod_uncurry A B C ∘ prod_curry = id.
 Proof.
-  simpl ; intros.
-  unfold prod_uncurry, prod_curry, compose.
-  extensionality x ; extensionality y ; extensionality z.
+  intros.
   reflexivity.
 Qed.
 
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