(* -*- coding: utf-8 -*- *)
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(*         *      The Rocq Prover / The Rocq Development Team           *)
(*  v      *         Copyright INRIA, CNRS and contributors             *)
(* <O___,, * (see version control and CREDITS file for authors & dates) *)
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(*    //   *    This file is distributed under the terms of the         *)
(*         *     GNU Lesser General Public License Version 2.1          *)
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(** * Proofs about standard combinators, exports functional extensionality.  Author: Matthieu Sozeau Institution: LRI, CNRS UMR 8623 - University Paris Sud *)
Require Export FunctionalExtensionality.
Open Scope program_scope.
(** Composition has [id] for neutral element and is associative. *)

(* Specifications: *)
Lemma compose_id_left : forall A B (f : A -> B), id ∘ f = f.
Lemma compose_id_right : forall A B (f : A -> B), f ∘ id = f.
Lemma compose_assoc : forall A B C D (f : A -> B) (g : B -> C) (h : C -> D),
h ∘ g ∘ f = h ∘ (g ∘ f).