From a8f65af5185fe60be2af279e39e5fe28d4fda2f1 Mon Sep 17 00:00:00 2001 From: Robbert Krebbers <mail@robbertkrebbers.nl> Date: Wed, 23 May 2018 18:59:49 +0200 Subject: [PATCH] Misc results about `Qp` fractions. --- theories/numbers.v | 6 ++++++ 1 file changed, 6 insertions(+) diff --git a/theories/numbers.v b/theories/numbers.v index 1eb8e1fc..28227372 100644 --- a/theories/numbers.v +++ b/theories/numbers.v @@ -608,6 +608,12 @@ Lemma Qp_div_2 x : (x / 2 + x / 2 = x)%Qp. Proof. change 2%positive with (2 * 1)%positive. by rewrite Qp_div_S, Qp_div_1. Qed. +Lemma Qp_half_half : (1 / 2 + 1 / 2 = 1)%Qp. +Proof. apply (bool_decide_unpack _); by compute. Qed. +Lemma Qp_quarter_three_quarter : (1 / 4 + 3 / 4 = 1)%Qp. +Proof. apply (bool_decide_unpack _); by compute. Qed. +Lemma Qp_three_quarter_quarter : (3 / 4 + 1 / 4 = 1)%Qp. +Proof. apply (bool_decide_unpack _); by compute. Qed. Lemma Qp_lt_sum (x y : Qp) : (x < y)%Qc ↔ ∃ z, y = (x + z)%Qp. Proof. -- GitLab