Reorganized HoTT_Base, updated theories

1 files changed, 4 insertions, 4 deletions

diff --git a/Empty.thy b/Empty.thy
index 1b339ba..107f2d7 100644
--- a/Empty.thy
+++ b/Empty.thy
@@ -14,12 +14,12 @@ section \<open>Constants and type rules\<close>
 section \<open>Empty type\<close>
 
 axiomatization
-  Empty :: Term  ("\<zero>") and
-  indEmpty :: "Term \<Rightarrow> Term"  ("(1ind\<^sub>\<zero>)")
+  Empty :: t  ("\<zero>") and
+  indEmpty :: "t \<Rightarrow> t"  ("(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:"