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{-# 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 = {!!}