(* * Copyright (c) 2009-2010, Andrew Appel, Robert Dockins and Aquinas Hobor. * *)
(** This library reexports portions of the Coq standard libraries used throughtout the proof.  It also defines some convenience tactics. *)
Require Export VST.msl.Extensionality.
Require Export Coq.Lists.List.
Require Export Coq.Bool.Bool.
Require Export Coq.Relations.Relations.
Require Export Omega.
Definition compose (A B C:Type) (g:B -> C) (f:A -> B) := fun x => g (f x).
Arguments compose [A B C] _ _ _.
Infix "oo" := compose (at level 54, right associativity).

Lemma bij_gf_id: forall {A B} (f: bijection A B),
(bij_g _ _ f) oo (bij_f _ _ f) = id _.