diff options
author | Stephane Glondu <steph@glondu.net> | 2012-01-12 16:02:20 +0100 |
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committer | Stephane Glondu <steph@glondu.net> | 2012-01-12 16:02:20 +0100 |
commit | 97fefe1fcca363a1317e066e7f4b99b9c1e9987b (patch) | |
tree | 97ec6b7d831cc5fb66328b0c63a11db1cbb2f158 /theories/Numbers/BigNumPrelude.v | |
parent | 300293c119981054c95182a90c829058530a6b6f (diff) |
Imported Upstream version 8.4~betaupstream/8.4_beta
Diffstat (limited to 'theories/Numbers/BigNumPrelude.v')
-rw-r--r-- | theories/Numbers/BigNumPrelude.v | 10 |
1 files changed, 4 insertions, 6 deletions
diff --git a/theories/Numbers/BigNumPrelude.v b/theories/Numbers/BigNumPrelude.v index 510b6888..26850688 100644 --- a/theories/Numbers/BigNumPrelude.v +++ b/theories/Numbers/BigNumPrelude.v @@ -1,6 +1,6 @@ (************************************************************************) (* 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 *) @@ -8,8 +8,6 @@ (* Benjamin Gregoire, Laurent Thery, INRIA, 2007 *) (************************************************************************) -(*i $Id: BigNumPrelude.v 14641 2011-11-06 11:59:10Z herbelin $ i*) - (** * BigNumPrelude *) (** Auxillary functions & theorems used for arbitrary precision efficient @@ -102,7 +100,7 @@ Hint Resolve Zlt_gt Zle_ge Z_div_pos: zarith. intros b x y (Hx1,Hx2) (Hy1,Hy2);split;auto with zarith. apply Zle_trans with ((b-1)*(b-1)). apply Zmult_le_compat;auto with zarith. - apply Zeq_le;ring. + apply Zeq_le; ring. Qed. Lemma sum_mul_carry : forall xh xl yh yl wc cc beta, @@ -315,7 +313,7 @@ Theorem Zmod_le_first: forall a b, 0 <= a -> 0 < b -> 0 <= a mod b <= a. apply Zdiv_le_lower_bound;auto with zarith. replace (2^p) with 0. destruct x;compute;intro;discriminate. - destruct p;trivial;discriminate z. + destruct p;trivial;discriminate. Qed. Lemma div_lt : forall p x y, 0 <= x < y -> x / 2^p < y. @@ -327,7 +325,7 @@ Theorem Zmod_le_first: forall a b, 0 <= a -> 0 < b -> 0 <= a mod b <= a. assert (0 < 2^p);auto with zarith. replace (2^p) with 0. destruct x;change (0<y);auto with zarith. - destruct p;trivial;discriminate z. + destruct p;trivial;discriminate. Qed. Theorem Zgcd_div_pos a b: |