add hott book files

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Michael Zhang 2023-05-16 22:23:32 -05:00
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```
module HottBook.Chapter2 where
```

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```
module HottBook.Chapter2Exercises where
open import Relation.Binary.PropositionalEquality
Type = Set
transport = subst
```
## Exercise 2.4
Define, by induction on n, a general notion of n-dimensional path in a type A,
simultaneously with the type of boundaries for such paths.
(tracked in [#6][6])
[6]: https://git.mzhang.io/school/cubical/issues/6
```
```
## Exercise 2.5
Prove that the functions [2.3.6] and (2.3.7) are inverse equivalences.
[2.3.6]: https://hott.github.io/book/hott-ebook-1357-gbe0b8e2.pdf#equation.2.3.6
[2.3.7]: https://hott.github.io/book/hott-ebook-1357-gbe0b8e2.pdf#equation.2.3.7
Here is the definition of transportconst from lemma 2.3.5:
```
transportconst : {A : Type} {x y : A} (B : Type) → (p : x ≡ y) → (b : B)
→ transport (λ _ → B) p b ≡ b
transportconst {A} {x} B p b =
let
D : (x y : A) → (p : x ≡ y) → Type
D x y p = transport (λ _ → B) p b ≡ b
d : (x : A) → D x x refl
d x = refl
in
J (λ x p → transport (λ _ → B) p b ≡ b) p (d x)
```