From a7b46d4b0204571ba9124accebc84f77ae0bed26 Mon Sep 17 00:00:00 2001
From: Josh Chen
Date: Thu, 30 Aug 2018 00:45:08 +0200
Subject: Add leq relation to meta-ordinals, it helps with proofs

---
 Empty.thy | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

(limited to 'Empty.thy')

diff --git a/Empty.thy b/Empty.thy
index 1b339ba..8f5cc8c 100644
--- a/Empty.thy
+++ b/Empty.thy
@@ -17,7 +17,7 @@ axiomatization
   Empty :: Term  ("\<zero>") and
   indEmpty :: "Term \<Rightarrow> Term"  ("(1ind\<^sub>\<zero>)")
 where
-  Empty_form: "\<zero> : U(O)"
+  Empty_form: "\<zero>: U(O)"
 and
   Empty_elim: "\<lbrakk>C: \<zero> \<longrightarrow> U(i); z: \<zero>\<rbrakk> \<Longrightarrow> ind\<^sub>\<zero>(z): C(z)"
 
-- 
cgit v1.2.3


From 9b17aac85aa650a7a9d6463d3d01f1eb228d4572 Mon Sep 17 00:00:00 2001
From: Josh Chen
Date: Tue, 11 Sep 2018 08:59:16 +0200
Subject: Go back to higher-order application notation

---
 Empty.thy | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

(limited to 'Empty.thy')

diff --git a/Empty.thy b/Empty.thy
index 8f5cc8c..a42f7ff 100644
--- a/Empty.thy
+++ b/Empty.thy
@@ -17,9 +17,9 @@ axiomatization
   Empty :: Term  ("\<zero>") and
   indEmpty :: "Term \<Rightarrow> Term"  ("(1ind\<^sub>\<zero>)")
 where
-  Empty_form: "\<zero>: U(O)"
+  Empty_form: "\<zero>: U O"
 and
-  Empty_elim: "\<lbrakk>C: \<zero> \<longrightarrow> U(i); z: \<zero>\<rbrakk> \<Longrightarrow> ind\<^sub>\<zero>(z): C(z)"
+  Empty_elim: "\<lbrakk>C: \<zero> \<longrightarrow> U i; z: \<zero>\<rbrakk> \<Longrightarrow> ind\<^sub>\<zero> z: C z"
 
 
 text "Rule attribute declarations:"
-- 
cgit v1.2.3

