From 56d6207d07b14aad71056c3d999da5b6964b2d2a Mon Sep 17 00:00:00 2001
From: Dan Frumin <dfrumin@cs.ru.nl>
Date: Wed, 16 Aug 2017 17:13:08 +0200
Subject: [PATCH] Circle is Kuratowski-finite

---
 FiniteSets/variations/k_finite.v | 11 +++++++++++
 1 file changed, 11 insertions(+)

diff --git a/FiniteSets/variations/k_finite.v b/FiniteSets/variations/k_finite.v
index 0852624..875dbcb 100644
--- a/FiniteSets/variations/k_finite.v
+++ b/FiniteSets/variations/k_finite.v
@@ -133,4 +133,15 @@ Section k_properties.
     apply fmap_isIn.
     apply (HXf x).
   Defined.
+
+  Lemma S1_Kfinite : Kf S1.
+  Proof.
+    apply Kf_unfold.
+    exists {|base|}.
+    intro a. simpl.
+    simple refine (S1_ind (fun z => Trunc (-1) (z = base)) _ _ a); simpl.
+    - apply (tr loop).
+    - apply path_ishprop.
+  Defined.
+
 End k_properties.