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Structures: Pi -> pi

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Rachel Lambda Samuelsson 2022-10-09 01:13:18 +02:00
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src/CwF/Structures.lagda.md
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@ -5,9 +5,9 @@ open import CwF.Base
module CwF.Structures where
```
This file defines several additional structures a CwF might have, such as Pi types, universes, sigma types, and identity types.
This file defines several additional structures a CwF might have, such as pi types, universes, sigma types, and identity types.
First are Pi types, because a type theory without them are pretty uninteresting.
First are pi types, because a type theory without them are pretty uninteresting.
```
record has-Pi {o h f : _} {𝓒 : Precategory o h}
(cwf : is-CwF {o} {h} {f} 𝓒) : Type (lsuc (o ⊔ h ⊔ f)) where
@ -71,4 +71,4 @@ Lastly comes the star of the show, $\beta$ reduction.
Cβ : {Γ : Ob} (A : ∣ Ty Γ ∣) (B : ∣ Ty (Γ ; A) ∣) (b : ∣ Tr (Γ ; A) B ∣)
(a : ∣ Tr Γ A ∣)
→ app (Cλ A B b) a ≡ b [ ⟨id, a ⟩ ]
```
```