From e513fc2958133e3a00c06ebcd1214741843acf08 Mon Sep 17 00:00:00 2001
From: Josh Chen
Date: Wed, 3 Jun 2020 13:09:30 +0200
Subject: 1. Type information context data 2. Small reformulations of rules 3.
 Bool

---
 spartan/data/List.thy       | 6 +++---
 spartan/data/More_Types.thy | 8 ++++++++
 2 files changed, 11 insertions(+), 3 deletions(-)

(limited to 'spartan/data')

diff --git a/spartan/data/List.thy b/spartan/data/List.thy
index 8fdaa1d..1798a23 100644
--- a/spartan/data/List.thy
+++ b/spartan/data/List.thy
@@ -52,14 +52,14 @@ abbreviation "ListRec A C \<equiv> ListInd A (\<lambda>_. C)"
 
 Lemma (derive) ListCase:
   assumes
-    "A: U i" "\<And>xs. xs: List A \<Longrightarrow> C xs: U i" and
+    "xs: List A" and
     nil_case: "c\<^sub>0: C (nil A)" and
     cons_case: "\<And>x xs. \<lbrakk>x: A; xs: List A\<rbrakk> \<Longrightarrow> f x xs: C (cons A x xs)" and
-    "xs: List A"
+    "\<And>xs. xs: List A \<Longrightarrow> C xs: U i"
   shows "?List_cases A (\<lambda>xs. C xs) c\<^sub>0 (\<lambda>x xs. f x xs) xs: C xs"
   by (elim xs) (fact nil_case, rule cons_case)
 
-lemmas List_cases [cases] = ListCase[rotated 4]
+lemmas List_cases [cases] = ListCase[unfolded ListCase_def]
 
 
 section \<open>Notation\<close>
diff --git a/spartan/data/More_Types.thy b/spartan/data/More_Types.thy
index 625f639..1d7abb9 100644
--- a/spartan/data/More_Types.thy
+++ b/spartan/data/More_Types.thy
@@ -90,6 +90,14 @@ definition "Bool \<equiv> \<top> \<or> \<top>"
 definition "true \<equiv> inl \<top> \<top> tt"
 definition "false \<equiv> inr \<top> \<top> tt"
 
+Lemma
+  BoolF: "Bool: U i" and
+  Bool_true: "true: Bool" and
+  Bool_false: "false: Bool"
+  unfolding Bool_def true_def false_def by typechk+
+
+lemmas [intros] = BoolF Bool_true Bool_false
+
 \<comment> \<open>Can define if-then-else etc.\<close>
 
 
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