proposition: Lemma GRP_dagger_laws : dagger_laws GRP_dagger_structure.
proof: Proof. repeat split ; intro ; intros ; use inverse_unique_precat. - exact (identity x). - apply groupoid_is_pregroupoid. - apply is_inverse_in_precat_identity. - exact (f · g). - apply groupoid_is_pregroupoid. - apply is_inverse_in_precat_comp ; apply groupoid_is_pregroupoid. - apply groupoid_is_pregroupoid ; exact f. - apply groupoid_is_pregroupoid. - apply is_inverse_in_precat_inv ; apply groupoid_is_pregroupoid. 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.Core.Univalence UniMath.CategoryTheory.Groupoids UniMath.CategoryTheory.DaggerCategories.Categories UniMath.CategoryTheory.DaggerCategories.Unitary UniMath.CategoryTheory.DaggerCategories.Univalence