diff options
author | Josh Chen | 2018-09-19 11:57:22 +0200 |
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committer | Josh Chen | 2018-09-19 11:57:22 +0200 |
commit | 1305c6beca2448156b61649da1a719d055aaf7f7 (patch) | |
tree | 81f1ea81350a70cfa27269c41f59e8640f9fd65a /Nat.thy | |
parent | f602cb54b39b3c1bb4f755db09bdeeb2f31a9559 (diff) |
Not sure what advantage is provided by having eta-expanded forms in the rules. Removing for now.
Diffstat (limited to '')
-rw-r--r-- | Nat.thy | 6 |
1 files changed, 3 insertions, 3 deletions
@@ -28,18 +28,18 @@ where a: C 0; n: \<nat>; C: \<nat> \<longrightarrow> U i; - \<And>n c. \<lbrakk>n: \<nat>; c: C n\<rbrakk> \<Longrightarrow> f n c: C (succ n) \<rbrakk> \<Longrightarrow> ind\<^sub>\<nat> (\<lambda>n c. f n c) a n: C n" and + \<And>n c. \<lbrakk>n: \<nat>; c: C n\<rbrakk> \<Longrightarrow> f n c: C (succ n) \<rbrakk> \<Longrightarrow> ind\<^sub>\<nat> f a n: C n" and Nat_comp_0: "\<lbrakk> a: C 0; C: \<nat> \<longrightarrow> U i; - \<And>n c. \<lbrakk>n: \<nat>; c: C(n)\<rbrakk> \<Longrightarrow> f n c: C (succ n) \<rbrakk> \<Longrightarrow> ind\<^sub>\<nat> (\<lambda>n c. f n c) a 0 \<equiv> a" and + \<And>n c. \<lbrakk>n: \<nat>; c: C(n)\<rbrakk> \<Longrightarrow> f n c: C (succ n) \<rbrakk> \<Longrightarrow> ind\<^sub>\<nat> f a 0 \<equiv> a" and Nat_comp_succ: "\<lbrakk> a: C 0; n: \<nat>; C: \<nat> \<longrightarrow> U i; - \<And>n c. \<lbrakk>n: \<nat>; c: C n\<rbrakk> \<Longrightarrow> f n c: C (succ n) \<rbrakk> \<Longrightarrow> ind\<^sub>\<nat> (\<lambda>n c. f n c) a (succ n) \<equiv> f n (ind\<^sub>\<nat> f a n)" + \<And>n c. \<lbrakk>n: \<nat>; c: C n\<rbrakk> \<Longrightarrow> f n c: C (succ n) \<rbrakk> \<Longrightarrow> ind\<^sub>\<nat> f a (succ n) \<equiv> f n (ind\<^sub>\<nat> f a n)" lemmas Nat_form [form] lemmas Nat_routine [intro] = Nat_form Nat_intro_0 Nat_intro_succ Nat_elim |