module Exercises1 where

open import Agda.Primitive

open import foundation-core.empty-types
open import foundation-core.equivalences
open import foundation-core.negation
open import foundation.dependent-pair-types
open import foundation.identity-types
open import foundation.univalence
open import foundation.sections
open import foundation.retractions

_≡_ = _＝_
⊥ = empty

equal-to-zero : {A : Set} (f : ¬ A) → A ≡ ⊥
equal-to-zero {A} f = eq-equiv A ⊥ eqv 
  where
    s : section f
    s = (λ ()) , λ x → ex-falso x

    r : retraction f
    r = (λ ()) , λ x → ex-falso (f x)

    eqv : A ≃ ⊥
    eqv = f , s , r