diff options
Diffstat (limited to 'theories/QArith/Qreduction.v')
| -rw-r--r-- | theories/QArith/Qreduction.v | 26 |
1 files changed, 25 insertions, 1 deletions
diff --git a/theories/QArith/Qreduction.v b/theories/QArith/Qreduction.v index 340cac83..9c522f09 100644 --- a/theories/QArith/Qreduction.v +++ b/theories/QArith/Qreduction.v @@ -6,7 +6,7 @@ (* * GNU Lesser General Public License Version 2.1 *) (************************************************************************) -(*i $Id: Qreduction.v 9245 2006-10-17 12:53:34Z notin $ i*) +(*i $Id: Qreduction.v 10739 2008-04-01 14:45:20Z herbelin $ i*) (** Normalisation functions for rational numbers. *) @@ -145,6 +145,7 @@ Qed. Definition Qplus' (p q : Q) := Qred (Qplus p q). Definition Qmult' (p q : Q) := Qred (Qmult p q). +Definition Qminus' x y := Qred (Qminus x y). Lemma Qplus'_correct : forall p q : Q, (Qplus' p q)==(Qplus p q). Proof. @@ -156,6 +157,11 @@ Proof. intros; unfold Qmult' in |- *; apply Qred_correct; auto. Qed. +Lemma Qminus'_correct : forall p q : Q, (Qminus' p q)==(Qminus p q). +Proof. + intros; unfold Qminus' in |- *; apply Qred_correct; auto. +Qed. + Add Morphism Qplus' : Qplus'_comp. Proof. intros; unfold Qplus' in |- *. @@ -167,3 +173,21 @@ Add Morphism Qmult' : Qmult'_comp. rewrite H; rewrite H0; auto with qarith. Qed. +Add Morphism Qminus' : Qminus'_comp. + intros; unfold Qminus' in |- *. + rewrite H; rewrite H0; auto with qarith. +Qed. + +Lemma Qred_opp: forall q, Qred (-q) = - (Qred q). +Proof. + intros (x, y); unfold Qred; simpl. + rewrite Zggcd_opp; case Zggcd; intros p1 (p2, p3); simpl. + unfold Qopp; auto. +Qed. + +Theorem Qred_compare: forall x y, + Qcompare x y = Qcompare (Qred x) (Qred y). +Proof. + intros x y; apply Qcompare_comp; apply Qeq_sym; apply Qred_correct. +Qed. + |