This commit is contained in:
Michael Zhang 2024-09-12 00:43:14 -05:00
commit 596980e9ff
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_build
*.pdf

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{
"agdaMode.connection.commandLineOptions": "--safe --cubical --without-K",
"files.associations": {
"*.lagda.typ": "agda"
}
}

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cubical-hott.agda-lib Normal file
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include: src
depend: cubical

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src/Chapter1.agda Normal file
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src/Chapter2.lagda.typ Normal file
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```
module Chapter2 where
open import Cubical.Foundations.Prelude
```
=== Lemma 2.1.1
```
lemma2-1-1 : {A : Type} {x y : A}
(x y) (y x)
lemma2-1-1 p i = p (~ i)
```
=== Lemma 2.1.2
```
lemma2-1-2 : {A : Type} {x y z : A}
(x y) (y z) (x z)
lemma2-1-2 {x = x} p q i = hcomp where
j (i = i0) x
j (i = i1) q j
) (p i)
```
=== Lemma 2.1.4
```
module lemma2-1-4 where
variable
A : Type
x y z w : A
p : x y
q : y z
r : z w
```
+ #[
```
lemma2-1-4-i1 : p p refl
lemma2-1-4-i1 {A} {x} {y} {p} j i = hfill where
_ (i = i0) x
_ (i = i1) y
) (inS (p i)) j
-- lemma2-1-4-i2 : p refl p
-- lemma2-1-4-i2 {A} {x} {y} {p} j i = hfill where
-- _ (i = i0) x
-- _ (i = i1) y
-- ) (inS (p i)) {! i1 !}
postulate
lemma2-1-4-ii1 : (sym p) p refl
lemma2-1-4-ii2 : p (sym p) refl
lemma2-1-4-iii : sym (sym p) refl
lemma2-1-4-iv : p (q r) (p q) r
lemma2-1-4-iv i j = {! !}
```
]