diff options
Diffstat (limited to 'plugins/rtauto/Bintree.v')
| -rw-r--r-- | plugins/rtauto/Bintree.v | 16 |
1 files changed, 8 insertions, 8 deletions
diff --git a/plugins/rtauto/Bintree.v b/plugins/rtauto/Bintree.v index 77f8f834..98dd257d 100644 --- a/plugins/rtauto/Bintree.v +++ b/plugins/rtauto/Bintree.v @@ -1,6 +1,6 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2010 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2012 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) @@ -15,14 +15,14 @@ Open Scope positive_scope. Ltac clean := try (simpl; congruence). Lemma Gt_Psucc: forall p q, - (p ?= Psucc q) = Gt -> (p ?= q) = Gt. + (p ?= Pos.succ q) = Gt -> (p ?= q) = Gt. Proof. intros. rewrite <- Pos.compare_succ_succ. now apply Pos.lt_gt, Pos.lt_lt_succ, Pos.gt_lt. Qed. Lemma Psucc_Gt : forall p, - (Psucc p ?= p) = Gt. + (Pos.succ p ?= p) = Gt. Proof. intros. apply Pos.lt_gt, Pos.lt_succ_diag_r. Qed. @@ -181,7 +181,7 @@ mkStore {index:positive;contents:Tree}. Definition empty := mkStore xH Tempty. Definition push a S := -mkStore (Psucc (index S)) (Tadd (index S) a (contents S)). +mkStore (Pos.succ (index S)) (Tadd (index S) a (contents S)). Definition get i S := Tget i (contents S). @@ -214,7 +214,7 @@ intros a S. rewrite Tget_Tadd. rewrite Psucc_Gt. intro W. -change (get (Psucc (index S)) S =PNone). +change (get (Pos.succ (index S)) S =PNone). apply get_Full_Gt; auto. apply Psucc_Gt. Qed. @@ -248,7 +248,7 @@ forall x, get i S = PSome x -> Proof. intros i a S F x H. case_eq (i ?= index S);intro test. -rewrite (Pcompare_Eq_eq _ _ test) in H. +rewrite (Pos.compare_eq _ _ test) in H. rewrite (get_Full_Eq _ F) in H;congruence. rewrite <- H. rewrite (get_push_Full i a). @@ -260,13 +260,13 @@ Qed. Lemma Full_index_one_empty : forall S, Full S -> index S = 1 -> S=empty. intros [ind cont] F one; inversion F. reflexivity. -simpl index in one;assert (h:=Psucc_not_one (index S)). +simpl index in one;assert (h:=Pos.succ_not_1 (index S)). congruence. Qed. Lemma push_not_empty: forall a S, (push a S) <> empty. intros a [ind cont];unfold push,empty. -simpl;intro H;injection H; intros _ ; apply Psucc_not_one. +simpl;intro H;injection H; intros _ ; apply Pos.succ_not_1. Qed. Fixpoint In (x:A) (S:Store) (F:Full S) {struct F}: Prop := |