```
{-# OPTIONS --cubical-compatible #-}
module Padova2025.Explorations.Uncountability.Lawvere
  {A X : Set} (f : A → (A → X)) (g : X → X) where
```

# Lawvere's fixed point theorem

```
open import Padova2025.ProvingBasics.Equality.Base
open import Padova2025.ProvingBasics.Equality.General
open import Padova2025.ProvingBasics.Connectives.Existential
```

```
canary : A → X
canary = {!!}
```

```
fix : ∃[ a ] canary ≗ f a → ∃[ x ] g x ≡ x
fix = {!!}
```

```
fix₀ : ((h : A → X) → ∃[ a ] h ≗ f a) → ∃[ x ] g x ≡ x
fix₀ = {!!}
```