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Migrate _↔̇_ to the new Function hierarchy #1978

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Migrate _↔̇_ to the new Function hierarchy #1978

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6 changes: 5 additions & 1 deletion src/Function/Bundles.agda
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Expand Up @@ -29,6 +29,7 @@ open import Relation.Binary.PropositionalEquality.Core as ≡
using (_≡_)
import Relation.Binary.PropositionalEquality.Properties as ≡
open Setoid using (isEquivalence)
open import Relation.Unary using (Pred)

private
variable
Expand Down Expand Up @@ -312,7 +313,7 @@ module _ (From : Setoid a ℓ₁) (To : Setoid b ℓ₂) where
-- Bundles specialised for propositional equality
------------------------------------------------------------------------

infix 3 _⟶_ _↣_ _↠_ _⤖_ _⇔_ _↩_ _↪_ _↩↪_ _↔_
infix 3 _⟶_ _↣_ _↠_ _⤖_ _⇔_ _↩_ _↪_ _↩↪_ _↔_ _↔̇_
_⟶_ : Set a → Set b → Set _
A ⟶ B = Func (≡.setoid A) (≡.setoid B)

Expand Down Expand Up @@ -340,6 +341,9 @@ A ↩↪ B = BiInverse (≡.setoid A) (≡.setoid B)
_↔_ : Set a → Set b → Set _
A ↔ B = Inverse (≡.setoid A) (≡.setoid B)

_↔̇_ : ∀ {i} {I : Set i} → Pred I a → Pred I b → Set _
A ↔̇ B = ∀ {i} → A i ↔ B i

-- We now define some constructors for the above that
-- automatically provide the required congruency proofs.

Expand Down