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chore: bump agda (#371)
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Still need to merge my WIP branch that kills `Extensionality` and the
bulk of the hlevel tactic, but I want to get a CI run.
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plt-amy committed Apr 3, 2024
1 parent 7a2bc9f commit 9321ce6
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4 changes: 2 additions & 2 deletions .github/workflows/build.yml
Expand Up @@ -48,8 +48,8 @@ jobs:
uses: actions/cache@v4
with:
path: _build
key: shake-4-${{ env.shake_version }}-${{ github.run_id }}
restore-keys: shake-4-${{ env.shake_version }}-
key: shake-5-${{ env.shake_version }}-${{ github.run_id }}
restore-keys: shake-5-${{ env.shake_version }}-

- name: Build 🛠️
run: |
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14 changes: 7 additions & 7 deletions src/1Lab/Classical.lagda.md
Expand Up @@ -46,16 +46,16 @@ We show that these two statements are equivalent propositions.

```agda
LEM-is-prop : is-prop LEM
LEM-is-prop = hlevel!
LEM-is-prop = hlevel 1

DNE-is-prop : is-prop DNE
DNE-is-prop = hlevel!
DNE-is-prop = hlevel 1

LEM→DNE : LEM DNE
LEM→DNE lem P = Dec-elim _ (λ p _ p) (λ ¬p ¬¬p absurd (¬¬p ¬p)) (lem P)

DNE→LEM : DNE LEM
DNE→LEM dne P = dne (el (Dec ∣ P ∣) hlevel!) λ k k (no λ p k (yes p))
DNE→LEM dne P = dne (el (Dec ∣ P ∣) (hlevel 1)) λ k k (no λ p k (yes p))

LEM≃DNE : LEM ≃ DNE
LEM≃DNE = prop-ext LEM-is-prop DNE-is-prop LEM→DNE DNE→LEM
Expand Down Expand Up @@ -84,7 +84,7 @@ The weak law of excluded middle is also a proposition.

```agda
WLEM-is-prop : is-prop WLEM
WLEM-is-prop = hlevel!
WLEM-is-prop = hlevel 1
```

## The axiom of choice {defines="axiom-of-choice"}
Expand Down Expand Up @@ -151,7 +151,7 @@ gives us a section $\Sigma P \to 2$.
```agda
module _ (split : Surjections-split) (P : Ω) where
section : ∥ ((x : Susp ∣ P ∣) fibre 2→Σ x) ∥
section = split Bool-is-set (Susp-prop-is-set hlevel!) 2→Σ 2→Σ-surjective
section = split Bool-is-set (Susp-prop-is-set (hlevel 1)) 2→Σ 2→Σ-surjective
```

But a section is always injective, and the booleans are [[discrete]], so we can
Expand All @@ -160,11 +160,11 @@ is equivalent to $P$, this concludes the proof.

```agda
Discrete-ΣP : Discrete (Susp ∣ P ∣)
Discrete-ΣP = ∥-∥-rec (Dec-is-hlevel 1 (Susp-prop-is-set hlevel! _ _))
Discrete-ΣP = ∥-∥-rec (Dec-is-hlevel 1 (Susp-prop-is-set (hlevel 1) _ _))
(λ f Discrete-inj (fst ∘ f) (right-inverse→injective 2→Σ (snd ∘ f))
Discrete-Bool)
section

AC→LEM : Dec ∣ P ∣
AC→LEM = Dec-≃ (Susp-prop-path hlevel!) Discrete-ΣP
AC→LEM = Dec-≃ (Susp-prop-path (hlevel 1)) Discrete-ΣP
```
1 change: 0 additions & 1 deletion src/1Lab/Equiv/HalfAdjoint.lagda.md
Expand Up @@ -7,7 +7,6 @@ description: |
---
<!--
```agda
{-# OPTIONS -vtc.def.fun:10 #-}
open import 1Lab.Reflection.Marker
open import 1Lab.HLevel.Closure
open import 1Lab.Path.Groupoid
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