------------------------------------------------------------------------
-- The Agda standard library
--
-- Heterogeneous equality
------------------------------------------------------------------------
 
-- This file contains some core definitions which are reexported by
-- Relation.Binary.HeterogeneousEquality.
 
{-# OPTIONS --with-K --safe #-}
 
module Relation.Binary.HeterogeneousEquality.Core where
 
open import Level using (Level)
open import Relation.Binary.PropositionalEquality.Core using (_≡_; refl)
 
private
  variable
    a b : Level
    A : Set a
 
------------------------------------------------------------------------
-- Heterogeneous equality
 
infix  _≅_
 
data _≅_ {A : Set a} (x : A) : {B : Set b} → B → Set a where
   refl : x ≅ x
 
------------------------------------------------------------------------
-- Conversion
 
≅-to-≡ : ∀ {x y : A} → x ≅ y → x ≡ y
≅-to-≡ refl = refl
 
≡-to-≅ : ∀ {x y : A} → x ≡ y → x ≅ y
≡-to-≅ refl = refl