Investigations on graph-theoretical constructions in Homotopy type theory

{-# OPTIONS --without-K --exact-split #-}

module lib.graph-definitions.Graph.isGroupoid
  where
  open import foundations.Core
  open import lib.graph-definitions.Graph
  open import lib.graph-definitions.Graph.EquivalencePrinciple
  open import lib.graph-calculation-reasoning.Isos
  open import lib.graph-relations.Isomorphic.isSet

  Graph-is-groupoid : ∀ {ℓ : Level} → isGroupoid (Graph ℓ)
  Graph-is-groupoid G H =
    let open EquivPrinciple G H in
    is-set-equiv-to-set (≃-sym (equiv-principle)) (≅-is-set G H)

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