diff options
| author | Josh Chen | 2018-09-20 21:35:51 +0200 |
|---|---|---|
| committer | Josh Chen | 2018-09-20 21:35:51 +0200 |
| commit | 55c148073df8de5f0cf4c45db23d2e3da7f4f093 (patch) | |
| tree | a17e2669b259f5b4ba543195ed8e86497455b822 /Equality.thy | |
| parent | 0bceaa97dfc4899ec2489dc3f2cd2ea11f5ae358 (diff) | |
Derive can prove pathcomp_comp. Fix typo.
Diffstat (limited to '')
| -rw-r--r-- | Equality.thy | 16 |
1 files changed, 1 insertions, 15 deletions
diff --git a/Equality.thy b/Equality.thy index 05ccbff..851c569 100644 --- a/Equality.thy +++ b/Equality.thy @@ -51,21 +51,7 @@ by (routine add: assms pathcomp_type) lemma pathcomp_comp: assumes "A: U i" and "a: A" shows "(refl a) \<bullet> (refl a) \<equiv> refl a" -unfolding pathcomp_def proof compute - show "(ind\<^sub>= (\<lambda>_. \<^bold>\<lambda>q. ind\<^sub>= (\<lambda>x. refl x) q) (refl a))`(refl a) \<equiv> refl a" - proof compute - show "\<^bold>\<lambda>q. (ind\<^sub>= (\<lambda>x. refl x) q): a =\<^sub>A a \<rightarrow> a =\<^sub>A a" - by (routine add: assms) - - show "(\<^bold>\<lambda>q. (ind\<^sub>= (\<lambda>x. refl x) q))`(refl a) \<equiv> refl a" - proof compute - show "\<And>q. q: a =\<^sub>A a \<Longrightarrow> ind\<^sub>= (\<lambda>x. refl x) q: a =\<^sub>A a" by (routine add: assms) - qed (derive lems: assms) - qed (routine add: assms) - - show "\<And>p. p: a =\<^sub>A a \<Longrightarrow> ind\<^sub>= (\<lambda>_. \<^bold>\<lambda>q. ind\<^sub>= (\<lambda>x. refl x) q) p: a =\<^sub>A a \<rightarrow> a =\<^sub>A a" - by (routine add: assms) -qed (routine add: assms) +unfolding pathcomp_def by (derive lems: assms) declare pathcomp_type [intro] |