From dfa56fb57b09296cdf311ec5972d2d33b787e48c Mon Sep 17 00:00:00 2001 From: Raphaël Monat Date: Tue, 3 Oct 2017 16:20:08 +0200 Subject: Add Qabs_Qinv: Qabs (/ q) == / (Qabs q). --- theories/QArith/Qabs.v | 7 +++++++ 1 file changed, 7 insertions(+) (limited to 'theories') diff --git a/theories/QArith/Qabs.v b/theories/QArith/Qabs.v index 116aa0d42..ec2ac7832 100644 --- a/theories/QArith/Qabs.v +++ b/theories/QArith/Qabs.v @@ -100,6 +100,13 @@ rewrite Z.abs_mul. reflexivity. Qed. +Lemma Qabs_Qinv : forall q, Qabs (/ q) == / (Qabs q). +Proof. + intros [n d]; simpl. + unfold Qinv. + case_eq n; intros; simpl in *; apply Qeq_refl. +Qed. + Lemma Qabs_Qminus x y: Qabs (x - y) = Qabs (y - x). Proof. unfold Qminus, Qopp. simpl. -- cgit v1.2.3