From dc2730916482bd230f9bd5244b8b2cc9d005f69a Mon Sep 17 00:00:00 2001
From: Josh Chen
Date: Tue, 7 Aug 2018 12:30:59 +0200
Subject: Old application syntax incompatible with Eisbach

---
 Coprod.thy | 40 ++++++++++++++++++++--------------------
 1 file changed, 20 insertions(+), 20 deletions(-)

(limited to 'Coprod.thy')

diff --git a/Coprod.thy b/Coprod.thy
index 75e621a..a301e7e 100644
--- a/Coprod.thy
+++ b/Coprod.thy
@@ -14,43 +14,43 @@ section \<open>Constants and type rules\<close>
 
 axiomatization
   Coprod :: "[Term, Term] \<Rightarrow> Term"  (infixr "+" 50) and
-  inl :: "Term \<Rightarrow> Term"  ("(1inl'(_'))") and
-  inr :: "Term \<Rightarrow> Term"  ("(1inr'(_'))") and
-  indCoprod :: "[Term, Term, Typefam, Term \<Rightarrow> Term, Term \<Rightarrow> Term, Term] \<Rightarrow> Term"  ("(1ind\<^sub>+[_,/ _])")
+  inl :: "Term \<Rightarrow> Term" and
+  inr :: "Term \<Rightarrow> Term" and
+  indCoprod :: "[Term \<Rightarrow> Term, Term \<Rightarrow> Term, Term] \<Rightarrow> Term"  ("(1ind\<^sub>+)")
 where
-  Coprod_form: "\<And>i A B. \<lbrakk>A : U(i); B : U(i)\<rbrakk> \<Longrightarrow> A + B : U(i)"
+  Coprod_form: "\<And>i A B. \<lbrakk>A : U(i); B : U(i)\<rbrakk> \<Longrightarrow> A + B: U(i)"
 and
-  Coprod_intro1: "\<And>A B a b. \<lbrakk>a : A; b : B\<rbrakk> \<Longrightarrow> inl(a) : A + B"
+  Coprod_intro1: "\<And>A B a b. \<lbrakk>a : A; b : B\<rbrakk> \<Longrightarrow> inl(a): A + B"
 and
-  Coprod_intro2: "\<And>A B a b. \<lbrakk>a : A; b : B\<rbrakk> \<Longrightarrow> inr(b) : A + B"
+  Coprod_intro2: "\<And>A B a b. \<lbrakk>a : A; b : B\<rbrakk> \<Longrightarrow> inr(b): A + B"
 and
   Coprod_elim: "\<And>i A B C c d e. \<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);
-    e : A + B
-    \<rbrakk> \<Longrightarrow> ind\<^sub>+[A,B] C c d e : C e"
+    \<And>x. x: A \<Longrightarrow> c(x): C(inl(x));
+    \<And>y. y: B \<Longrightarrow> d(y): C(inr(y));
+    e: A + B
+    \<rbrakk> \<Longrightarrow> ind\<^sub>+(c)(d)(e) : C(e)"
 and
   Coprod_comp1: "\<And>i A B C c d a. \<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);
-    a : A
-    \<rbrakk> \<Longrightarrow> ind\<^sub>+[A,B] C c d inl(a) \<equiv> c a"
+    \<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)"
 and
   Coprod_comp2: "\<And>i A B C c d b. \<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);
-    b : B
-    \<rbrakk> \<Longrightarrow> ind\<^sub>+[A,B] C c d inr(b) \<equiv> d b"
+    \<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)"
 
 text "Admissible formation inference rules:"
 
 axiomatization where
-  Coprod_form_cond1: "\<And>i A B. A + B : U(i) \<Longrightarrow> A : U(i)"
+  Coprod_form_cond1: "\<And>i A B. A + B: U(i) \<Longrightarrow> A: U(i)"
 and
-  Coprod_form_cond2: "\<And>i A B. A + B : U(i) \<Longrightarrow> B : U(i)"
+  Coprod_form_cond2: "\<And>i A B. A + B: U(i) \<Longrightarrow> B: U(i)"
 
 lemmas Coprod_rules [intro] = Coprod_form Coprod_intro1 Coprod_intro2
                               Coprod_elim Coprod_comp1 Coprod_comp2
-- 
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