From d379e77dab3ff6a854b94af47be6098a2ba6ca64 Mon Sep 17 00:00:00 2001
From: Josh Chen
Date: Sat, 10 Apr 2021 21:59:42 +0100
Subject: start hprop stuff

---
 hott/Bool_HoTT.thy    |  8 ++++++++
 hott/Propositions.thy | 19 +++++++++++++++++++
 2 files changed, 27 insertions(+)
 create mode 100644 hott/Bool_HoTT.thy
 create mode 100644 hott/Propositions.thy

diff --git a/hott/Bool_HoTT.thy b/hott/Bool_HoTT.thy
new file mode 100644
index 0000000..57a57b7
--- /dev/null
+++ b/hott/Bool_HoTT.thy
@@ -0,0 +1,8 @@
+theory Bool_HoTT
+imports
+  MLTT.Prelude
+  Propositions
+
+begin
+
+end
diff --git a/hott/Propositions.thy b/hott/Propositions.thy
new file mode 100644
index 0000000..66e34d2
--- /dev/null
+++ b/hott/Propositions.thy
@@ -0,0 +1,19 @@
+theory Propositions
+imports
+  MLTT.Prelude
+  Equivalence
+
+begin
+
+definition isProp where "isProp A \<equiv> \<Prod>x y: A. x =\<^bsub>A\<^esub> y"
+definition isSet where "isSet A \<equiv> \<Prod>x y: A. \<Prod>p q: x =\<^bsub>A\<^esub> y. p =\<^bsub>x =\<^bsub>A\<^esub> y\<^esub> q"
+
+Theorem isProp_Top: "isProp \<top>"
+  unfolding isProp_def
+  by (intros, elims, refl)
+
+Theorem isProp_Bot: "isProp \<bottom>"
+  unfolding isProp_def
+  by (intros, elim)
+
+end
-- 
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