diff options
| author | Josh Chen | 2020-05-25 18:50:59 +0200 |
|---|---|---|
| committer | Josh Chen | 2020-05-25 18:50:59 +0200 |
| commit | 60f32406e8c9712c0689d54a3dd4f8e17d310d52 (patch) | |
| tree | 11fe176eb187a2f146060af1584005506f220c9d /hott | |
| parent | 80edbd08e13200d2c080ac281d19948bbbcd92e0 (diff) | |
Lists + more reorganizing
Diffstat (limited to 'hott')
| -rw-r--r-- | hott/HoTT.thy | 10 | ||||
| -rw-r--r-- | hott/Identity.thy | 4 | ||||
| -rw-r--r-- | hott/More_Types.thy (renamed from hott/Base.thy) | 10 | ||||
| -rw-r--r-- | hott/Nat.thy | 2 |
4 files changed, 14 insertions, 12 deletions
diff --git a/hott/HoTT.thy b/hott/HoTT.thy new file mode 100644 index 0000000..0b3040c --- /dev/null +++ b/hott/HoTT.thy @@ -0,0 +1,10 @@ +theory HoTT +imports + Identity + Equivalence + More_Types + Nat + +begin + +end diff --git a/hott/Identity.thy b/hott/Identity.thy index 3a982f6..3fef536 100644 --- a/hott/Identity.thy +++ b/hott/Identity.thy @@ -30,13 +30,13 @@ axiomatization where b: A; \<And>x y p. \<lbrakk>p: x =\<^bsub>A\<^esub> y; x: A; y: A\<rbrakk> \<Longrightarrow> C x y p: U i; \<And>x. x: A \<Longrightarrow> f x: C x x (refl x) - \<rbrakk> \<Longrightarrow> IdInd A (\<lambda>x y p. C x y p) f a b p: C a b p" and + \<rbrakk> \<Longrightarrow> IdInd A (\<lambda>x y p. C x y p) (\<lambda>x. f x) a b p: C a b p" and Id_comp: "\<lbrakk> a: A; \<And>x y p. \<lbrakk>x: A; y: A; p: x =\<^bsub>A\<^esub> y\<rbrakk> \<Longrightarrow> C x y p: U i; \<And>x. x: A \<Longrightarrow> f x: C x x (refl x) - \<rbrakk> \<Longrightarrow> IdInd A (\<lambda>x y p. C x y p) f a a (refl a) \<equiv> f a" + \<rbrakk> \<Longrightarrow> IdInd A (\<lambda>x y p. C x y p) (\<lambda>x. f x) a a (refl a) \<equiv> f a" lemmas [intros] = IdF IdI and diff --git a/hott/Base.thy b/hott/More_Types.thy index 610a373..17789f8 100644 --- a/hott/Base.thy +++ b/hott/More_Types.thy @@ -1,17 +1,9 @@ -theory Base +theory More_Types imports Equivalence begin -section \<open>Notation\<close> - -syntax "_dollar" :: \<open>logic \<Rightarrow> logic \<Rightarrow> logic\<close> (infixr "$" 3) -translations "a $ b" \<rightharpoonup> "a (b)" - -abbreviation (input) K where "K x \<equiv> \<lambda>_. x" - - section \<open>Sum type\<close> axiomatization diff --git a/hott/Nat.thy b/hott/Nat.thy index 311f2d9..e129be0 100644 --- a/hott/Nat.thy +++ b/hott/Nat.thy @@ -1,5 +1,5 @@ theory Nat -imports Base +imports Equivalence begin |