proposition: Proposition double_cat_weq_univalent_doublecategory_inv₁ (C : univalent_double_cat) : doublecategory_to_univalent_double_cat (double_cat_to_univalent_doublecategory C) = C.
proof: Proof. induction C as [ C1 H ]. use subtypePath. { intro. apply isapropdirprod ; repeat (use impred ; intro) ; apply isaset_disp_mor. } use total2_paths_f ; [ apply idpath | ]. use pathsdirprod. - use subtypePath. { intro. apply isaprop_double_lunitor_laws. } apply idpath. - use pathsdirprod. + use subtypePath. { intro. apply isaprop_double_runitor_laws. } apply idpath. + use subtypePath. { intro. apply isaprop_double_associator_laws. } apply idpath. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Prelude UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat UniMath.CategoryTheory.TwoSidedDisplayedCats.Isos UniMath.CategoryTheory.TwoSidedDisplayedCats.Univalence UniMath.Bicategories.Core.Bicat UniMath.Bicategories.DoubleCategories.Basics.DoubleCategoryBasics UniMath.Bicategories.DoubleCategories.Core.BicatOfDoubleCats UniMath.Bicategories.DoubleCategories.Core.DoubleCats UniMath.Bicategories.DoubleCategories.Core.UnivalentDoubleCats UniMath.Bicategories.DoubleCategories.AlternativeDefinitions.DoubleCatsUnfolded