-- inspired by https://github.com/agda/agda/issues/2556

postulate0 A : ★

def0 ZZ : ★ = 0 ≡ 0 : ℕ

def reflZ : ZZ = δ _ ⇒ 0


namespace erased {
  def0 ZZA : ★ = 0.ZZ → A

  def propeq : (x : ZZA) → x ≡ (λ _ ⇒ x reflZ) : ZZA =
    λ x ⇒ δ _ ⇒ x

  def defeq : 0.(P : ZZA → ★) → 0.(x : ZZA) → P (λ _ ⇒ x reflZ) → P x =
    λ P x p ⇒ p
}

namespace unrestricted {
  def0 ZZA : ★ = ω.ZZ → A

  def defeq : 0.(P : ZZA → ★) → 0.(x : ZZA) → P (λ _ ⇒ x reflZ) → P x =
    λ P x p ⇒ p
}

namespace linear {
  def0 ZZA : ★ = 1.ZZ → A

  #[fail "λ _ ⇒ x reflZ is not equal to x"]
  def defeq : 0.(P : ZZA → ★) → 0.(x : ZZA) → P (λ _ ⇒ x reflZ) → P x =
    λ P x p ⇒ p
}