From 9ea0e76f92383ab14859cd5857f5a3ef1acec2c0 Mon Sep 17 00:00:00 2001
From: Josh Chen
Date: Wed, 23 May 2018 08:26:37 +0200
Subject: pre-system upgrade commit

---
 HoTT_Test.thy | 58 ----------------------------------------------------------
 1 file changed, 58 deletions(-)
 delete mode 100644 HoTT_Test.thy

(limited to 'HoTT_Test.thy')

diff --git a/HoTT_Test.thy b/HoTT_Test.thy
deleted file mode 100644
index b37ac76..0000000
--- a/HoTT_Test.thy
+++ /dev/null
@@ -1,58 +0,0 @@
-theory HoTT_Test
-imports HoTT
-begin
-
-text \<open>Check trivial stuff:\<close>
-
-lemma "Null : U"
-  by (rule Null_form)
-
-lemma "\<lbrakk>A \<equiv> B; x : B\<rbrakk> \<Longrightarrow> x : A"
-proof -
-  assume "A \<equiv> B"
-  then have "B \<equiv> A" by (rule Pure.symmetric)
-  then have "x : B \<Longrightarrow> x :A"  by (rule equal_types)
-  oops
-(* qed---figure out how to discharge assumptions *)
-
-text \<open>
-Do functions behave like we expect them to?
-(Or, is my implementation at least somewhat correct?...
-\<close>
-
-\<comment> {* NOTE!!! The issues with substitution here.
-We need the HoTT term \<open>b\<close> and the type family \<open>B\<close> to indeed be a Pure \<lambda>-term!
-This seems to mean that I have to implement the HoTT types in more than one Pure type.
-See CTT.thy for examples.
-*}
-
-lemma "A \<equiv> B \<Longrightarrow> (\<^bold>\<lambda>x:A. x) : B\<rightarrow>A"
-proof -
-  have "A \<equiv> B \<Longrightarrow> B \<equiv> A" by (rule Pure.symmetric)
-  then have "\<And>x::Term. A \<equiv> B \<Longrightarrow> x : B \<Longrightarrow> x : A" by (rule equal_types)
-  thus "A \<equiv> B \<Longrightarrow> (\<^bold>\<lambda>x:A. x) : B\<rightarrow>A" by (rule Function_intro)
-qed
-
-lemma "\<^bold>\<lambda>x. \<^bold>\<lambda>y. x : A\<rightarrow>B\<rightarrow>A"
-proof -
-  have "\<And>x. x : A \<Longrightarrow> \<^bold>\<lambda>y. x : B \<rightarrow> A" by (rule Function_intro)
-  thus "\<^bold>\<lambda>x. \<^bold>\<lambda>y. x : A\<rightarrow>B\<rightarrow>A" by (rule Function_intro)
-qed
-
-text \<open>Here's a dumb proof that 2 is a natural number:\<close>
-
-lemma "succ(succ 0) : Nat"
-proof -
-  have "0 : Nat" by (rule Nat_intro1)
-  from this have "(succ 0) : Nat" by (rule Nat_intro2)
-  thus "succ(succ 0) : Nat" by (rule Nat_intro2)
-qed
-
-text \<open>
-We can of course iterate the above for as many applications of \<open>succ\<close> as we like.
-The next thing to do is to implement some kind of induction tactic to automate such proofs.
-
-When we get more stuff working, I'd like to aim for formalizing the encode-decode method.
-\<close>
-
-end
\ No newline at end of file
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