proposition: Lemma REL_dagger_laws : dagger_laws REL_dagger_structure.
proof: Proof. repeat split ; intro ; intros ; repeat (apply funextsec ; intro) ; cbn. - use (invweq (weqeqweqhProp _ _)). use weqimplimpl. + exact (λ p, ! p). + exact (λ p, ! p). + apply eqset. + apply eqset. - use (invweq (weqeqweqhProp _ _)). use weqimplimpl. + intro p. use (factor_through_squash_hProp _ _ p). clear p ; intro p. apply hinhpr. exact (pr1 p ,, pr22 p ,, pr12 p). + intro p. use (factor_through_squash_hProp _ _ p). clear p ; intro p. apply hinhpr. exact (pr1 p ,, pr22 p ,, pr12 p). + apply isapropishinh. + apply isapropishinh. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Categories.Rel UniMath.CategoryTheory.DaggerCategories.Categories UniMath.CategoryTheory.DaggerCategories.Unitary UniMath.CategoryTheory.DaggerCategories.Univalence