Interval is K-finite

2017-08-17 22:43:22 +02:00 · 2017-08-17 22:43:22 +02:00 · da60017367
parent 8ff54def39
commit da60017367
1 changed files with 12 additions and 1 deletions
--- a/FiniteSets/variations/k_finite.v
+++ b/FiniteSets/variations/k_finite.v
@ -143,5 +143,16 @@ Section k_properties.
    - apply (tr loop).
    - apply path_ishprop.
  Defined.
-
+  
+  Lemma I_Kfinite : Kf interval.
+  Proof.
+    apply Kf_unfold.
+    exists {|Interval.one|}.
+    intro a. simpl.
+    simple refine (interval_ind (fun z => Trunc (-1) (z = Interval.one)) _ _ _ a); simpl.
+    - apply (tr seg).
+    - apply (tr idpath).
+    - apply path_ishprop.
+  Defined.
+  
 End k_properties.