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 | |
| parent | 0bceaa97dfc4899ec2489dc3f2cd2ea11f5ae358 (diff) | |
Derive can prove pathcomp_comp. Fix typo.
| -rw-r--r-- | Equality.thy | 16 | ||||
| -rw-r--r-- | HoTT_Base.thy | 2 |
2 files changed, 2 insertions, 16 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] diff --git a/HoTT_Base.thy b/HoTT_Base.thy index 0b460d9..9e8fee7 100644 --- a/HoTT_Base.thy +++ b/HoTT_Base.thy @@ -53,7 +53,7 @@ text \<open> Using method @{method rule} with @{thm U_cumulative} is unsafe, if applied blindly it will typically lead to non-termination. One should instead use @{method elim}, or instantiate @{thm U_cumulative} suitably. -@{thm U_cumulative'} is an alternative rule used by the method \<open>lift\<close> in @{file HoTT_Methods.thy}. +@{thm U_cumulative'} is an alternative rule used by the method \<open>cumulativity\<close> in @{file HoTT_Methods.thy}. \<close> |