diff options
author | 2006-11-21 21:38:49 +0000 | |
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committer | 2006-11-21 21:38:49 +0000 | |
commit | 70b9be8acc1d1ada178a95c1cd4013506e9d0d1b (patch) | |
tree | f672a286d962cc67c95874b3b60402fc957870b6 /theories/QArith/Qreals.v | |
parent | a5bd4e097a94cc4f863bf4d4bcc5ce592c30ba47 (diff) | |
parent | 208a0f7bfa5249f9795e6e225f309cbe715c0fad (diff) |
Merge commit 'upstream/8.1.gamma' into 8.1
Diffstat (limited to 'theories/QArith/Qreals.v')
-rw-r--r-- | theories/QArith/Qreals.v | 26 |
1 files changed, 11 insertions, 15 deletions
diff --git a/theories/QArith/Qreals.v b/theories/QArith/Qreals.v index 5b7480c1..6bd161f3 100644 --- a/theories/QArith/Qreals.v +++ b/theories/QArith/Qreals.v @@ -6,12 +6,12 @@ (* * GNU Lesser General Public License Version 2.1 *) (************************************************************************) -(*i $Id: Qreals.v 8883 2006-05-31 21:56:37Z letouzey $ i*) +(*i $Id: Qreals.v 9245 2006-10-17 12:53:34Z notin $ i*) Require Export Rbase. Require Export QArith_base. -(** * A field tactic for rational numbers. *) +(** A field tactic for rational numbers. *) (** Since field cannot operate on setoid datatypes (yet?), we translate Q goals into reals before applying field. *) @@ -52,8 +52,9 @@ assert ((X1 * Y2)%R = (Y1 * X2)%R). unfold X1, X2, Y1, Y2 in |- *; do 2 rewrite <- mult_IZR. apply IZR_eq; auto. clear H. -field; auto. -rewrite <- H0; field; auto. +field_simplify_eq; auto. +ring_simplify X1 Y2 (Y2 * X1)%R. +rewrite H0 in |- *; ring. Qed. Lemma Rle_Qle : forall x y : Q, (Q2R x <= Q2R y)%R -> x<=y. @@ -176,16 +177,11 @@ unfold Qinv, Q2R, Qeq in |- *; intros (x1, x2); unfold Qden, Qnum in |- *. case x1. simpl in |- *; intros; elim H; trivial. intros; field; auto. -apply Rmult_integral_contrapositive; split; auto. -apply Rmult_integral_contrapositive; split; auto. -apply Rinv_neq_0_compat; auto. -intros; field; auto. -do 2 rewrite <- mult_IZR. -simpl in |- *; rewrite Pmult_comm; auto. -apply Rmult_integral_contrapositive; split; auto. -apply Rmult_integral_contrapositive; split; auto. -apply not_O_IZR; auto with qarith. -apply Rinv_neq_0_compat; auto. +intros; + change (IZR (Zneg x2)) with (- IZR (' x2))%R in |- *; + change (IZR (Zneg p)) with (- IZR (' p))%R in |- *; + field; (*auto 8 with real.*) + repeat split; auto; auto with real. Qed. Lemma Q2R_div : @@ -210,4 +206,4 @@ Goal forall x y : Q, ~ y==0#1 -> (x/y)*y == x. intros; QField. intro; apply H; apply eqR_Qeq. rewrite H0; unfold Q2R in |- *; simpl in |- *; field; auto with real. -Abort.
\ No newline at end of file +Abort. |