{-# OPTIONS --cubical-compatible --safe #-}
open import Relation.Binary.Bundles using (PartialSetoid)
module Relation.Binary.Reasoning.PartialSetoid
{s₁ s₂} (S : PartialSetoid s₁ s₂) where
open PartialSetoid S
import Relation.Binary.Reasoning.Base.Partial _≈_ trans as Base
open Base public
hiding (step-∼)
infixr 2 step-≈ step-≈˘
step-≈ = Base.step-∼
syntax step-≈ x y≈z x≈y = x ≈⟨ x≈y ⟩ y≈z
step-≈˘ : ∀ x {y z} → y IsRelatedTo z → y ≈ x → x IsRelatedTo z
step-≈˘ x y∼z y≈x = x ≈⟨ sym y≈x ⟩ y∼z
syntax step-≈˘ x y≈z y≈x = x ≈˘⟨ y≈x ⟩ y≈z