diff options
Diffstat (limited to 'theories/Lists/List.v')
| -rw-r--r-- | theories/Lists/List.v | 27 |
1 files changed, 16 insertions, 11 deletions
diff --git a/theories/Lists/List.v b/theories/Lists/List.v index 4c14008c..ecadddbc 100644 --- a/theories/Lists/List.v +++ b/theories/Lists/List.v @@ -1,14 +1,12 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2011 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2010 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) (************************************************************************) -(*i $Id: List.v 14641 2011-11-06 11:59:10Z herbelin $ i*) - -Require Import Le Gt Minus Min Bool. +Require Import Le Gt Minus Bool. Set Implicit Arguments. @@ -55,9 +53,16 @@ Section Lists. End Lists. -(* Keep these notations local to prevent conflicting notations *) -Local Notation "[ ]" := nil : list_scope. -Local Notation "[ a ; .. ; b ]" := (a :: .. (b :: []) ..) : list_scope. + +(** Standard notations for lists. +In a special module to avoid conflict. *) +Module ListNotations. +Notation " [ ] " := nil : list_scope. +Notation " [ x ] " := (cons x nil) : list_scope. +Notation " [ x ; .. ; y ] " := (cons x .. (cons y nil) ..) : list_scope. +End ListNotations. + +Import ListNotations. (** ** Facts about lists *) @@ -119,7 +124,7 @@ Section Facts. unfold not; intros a H; inversion_clear H. Qed. - Theorem in_split : forall x (l:list A), In x l -> exists l1, exists l2, l = l1++x::l2. + Theorem in_split : forall x (l:list A), In x l -> exists l1 l2, l = l1++x::l2. Proof. induction l; simpl; destruct 1. subst a; auto. @@ -254,7 +259,7 @@ Section Facts. Qed. - (** Compatibility wtih other operations *) + (** Compatibility with other operations *) Lemma app_length : forall l l' : list A, length (l++l') = length l + length l'. Proof. @@ -1643,7 +1648,7 @@ Proof. exact Forall2_nil. Qed. Theorem Forall2_app_inv_l : forall A B (R:A->B->Prop) l1 l2 l', Forall2 R (l1 ++ l2) l' -> - exists l1', exists l2', Forall2 R l1 l1' /\ Forall2 R l2 l2' /\ l' = l1' ++ l2'. + exists l1' l2', Forall2 R l1 l1' /\ Forall2 R l2 l2' /\ l' = l1' ++ l2'. Proof. induction l1; intros. exists [], l'; auto. @@ -1654,7 +1659,7 @@ Qed. Theorem Forall2_app_inv_r : forall A B (R:A->B->Prop) l1' l2' l, Forall2 R l (l1' ++ l2') -> - exists l1, exists l2, Forall2 R l1 l1' /\ Forall2 R l2 l2' /\ l = l1 ++ l2. + exists l1 l2, Forall2 R l1 l1' /\ Forall2 R l2 l2' /\ l = l1 ++ l2. Proof. induction l1'; intros. exists [], l; auto. |