diff options
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: |