Circle is Kuratowski-finite

2017-08-16 17:13:08 +02:00 · 2017-08-16 17:13:08 +02:00 · 56d6207d07
parent 809382ba13
commit 56d6207d07
1 changed files with 11 additions and 0 deletions
--- 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.