From f9c54965b2328f421792173ab92c27c8b752538e Mon Sep 17 00:00:00 2001
From: Zhen Zhang <izgzhen@gmail.com>
Date: Tue, 4 Oct 2016 15:27:57 +0200
Subject: [PATCH] Add lemmas about Qp and fraction

---
 theories/numbers.v | 7 +++++++
 1 file changed, 7 insertions(+)

diff --git a/theories/numbers.v b/theories/numbers.v
index c6549846..23e4697b 100644
--- a/theories/numbers.v
+++ b/theories/numbers.v
@@ -566,3 +566,10 @@ Proof.
   exists (mk_Qp (q2 - q1 / 2%Z) Hq2'). split; [by rewrite Qp_div_2|].
   apply Qp_eq; simpl. ring.
 Qed.
+
+Lemma Qp_ge_1 (q: Qp): ¬ ((1 + q)%Qp ≤ 1%Qp)%Qc.
+Proof.
+  intros Hle.
+  apply (Qcplus_le_mono_l q 0 1) in Hle.
+  apply Qcle_ngt in Hle. by destruct q.
+Qed.
-- 
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