diff options
Diffstat (limited to 'theories/Program/Combinators.v')
| -rw-r--r-- | theories/Program/Combinators.v | 22 |
1 files changed, 9 insertions, 13 deletions
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. |