1 files changed, 17 insertions, 17 deletions

diff --git a/Coprod.thy b/Coprod.thy
index 4607d1d..b87958a 100644
--- a/Coprod.thy
+++ b/Coprod.thy
@@ -17,40 +17,40 @@ axiomatization
   inr :: "Term \<Rightarrow> Term" and
   indCoprod :: "[Term \<Rightarrow> Term, Term \<Rightarrow> Term, Term] \<Rightarrow> Term"  ("(1ind\<^sub>+)")
 where
-  Coprod_form: "\<lbrakk>A: U(i); B: U(i)\<rbrakk> \<Longrightarrow> A + B: U(i)"
+  Coprod_form: "\<lbrakk>A: U i; B: U i\<rbrakk> \<Longrightarrow> A + B: U i"
 and
-  Coprod_intro_inl: "\<lbrakk>a: A; B: U(i)\<rbrakk> \<Longrightarrow> inl(a): A + B"
+  Coprod_intro_inl: "\<lbrakk>a: A; B: U i\<rbrakk> \<Longrightarrow> inl a: A + B"
 and
-  Coprod_intro_inr: "\<lbrakk>b: B; A: U(i)\<rbrakk> \<Longrightarrow> inr(b): A + B"
+  Coprod_intro_inr: "\<lbrakk>b: B; A: U i\<rbrakk> \<Longrightarrow> inr b: A + B"
 and
   Coprod_elim: "\<lbrakk>
-    C: A + B \<longrightarrow> U(i);
-    \<And>x. x: A \<Longrightarrow> c(x): C(inl(x));
-    \<And>y. y: B \<Longrightarrow> d(y): C(inr(y));
+    C: A + B \<longrightarrow> U i;
+    \<And>x. x: A \<Longrightarrow> c x: C (inl x);
+    \<And>y. y: B \<Longrightarrow> d y: C (inr y);
     u: A + B
-    \<rbrakk> \<Longrightarrow> ind\<^sub>+(c)(d)(u) : C(u)"
+    \<rbrakk> \<Longrightarrow> ind\<^sub>+ c d u : C u"
 and
   Coprod_comp_inl: "\<lbrakk>
-    C: A + B \<longrightarrow> U(i);
-    \<And>x. x: A \<Longrightarrow> c(x): C(inl(x));
-    \<And>y. y: B \<Longrightarrow> d(y): C(inr(y));
+    C: A + B \<longrightarrow> U i;
+    \<And>x. x: A \<Longrightarrow> c x: C (inl x);
+    \<And>y. y: B \<Longrightarrow> d y: C (inr y);
     a: A
-    \<rbrakk> \<Longrightarrow> ind\<^sub>+(c)(d)(inl(a)) \<equiv> c(a)"
+    \<rbrakk> \<Longrightarrow> ind\<^sub>+ c d (inl a) \<equiv> c a"
 and
   Coprod_comp_inr: "\<lbrakk>
-    C: A + B \<longrightarrow> U(i);
-    \<And>x. x: A \<Longrightarrow> c(x): C(inl(x));
-    \<And>y. y: B \<Longrightarrow> d(y): C(inr(y));
+    C: A + B \<longrightarrow> U i;
+    \<And>x. x: A \<Longrightarrow> c x: C (inl x);
+    \<And>y. y: B \<Longrightarrow> d y: C (inr y);
     b: B
-    \<rbrakk> \<Longrightarrow> ind\<^sub>+(c)(d)(inr(b)) \<equiv> d(b)"
+    \<rbrakk> \<Longrightarrow> ind\<^sub>+ c d (inr b) \<equiv> d b"
 
 
 text "Admissible formation inference rules:"
 
 axiomatization where
-  Coprod_wellform1: "A + B: U(i) \<Longrightarrow> A: U(i)"
+  Coprod_wellform1: "A + B: U i \<Longrightarrow> A: U i"
 and
-  Coprod_wellform2: "A + B: U(i) \<Longrightarrow> B: U(i)"
+  Coprod_wellform2: "A + B: U i \<Longrightarrow> B: U i"
 
 
 text "Rule attribute declarations:"