From 2e807b74bd0f4e9a2ccfcb861bef876dba5aa066 Mon Sep 17 00:00:00 2001
From: Josh Chen
Date: Sat, 30 May 2020 14:38:12 +0200
Subject: fix name

---
 hott/Nat.thy | 6 +++++-
 1 file changed, 5 insertions(+), 1 deletion(-)

(limited to 'hott/Nat.thy')

diff --git a/hott/Nat.thy b/hott/Nat.thy
index e8657a4..e36d6be 100644
--- a/hott/Nat.thy
+++ b/hott/Nat.thy
@@ -49,6 +49,8 @@ abbreviation "NatRec C \<equiv> NatInd (\<lambda>_. C)"
 
 section \<open>Basic arithmetic\<close>
 
+subsection \<open>Addition\<close>
+
 definition add (infixl "+" 120) where "m + n \<equiv> NatRec Nat n (K suc) m"
 
 lemma add_type [typechk]:
@@ -82,7 +84,7 @@ Lemma (derive) add_suc:
     \<guillemotright> vars _ ih by reduce (eq ih; intro)
   done
 
-Lemma (derive) suc_monotone:
+Lemma (derive) suc_eq:
   assumes "m: Nat" "n: Nat"
   shows "p: m = n \<Longrightarrow> suc m = suc n"
   by (eq p) intro
@@ -108,6 +110,8 @@ Lemma (derive) add_comm:
       qed
   done
 
+subsection \<open>Multiplication\<close>
+
 definition mul (infixl "*" 120) where
   [comps]: "m * n \<equiv> NatRec Nat 0 (K $ add n) m"
 
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