proposition: Lemma disp_id_pstrans_laws : is_disp_pstrans _ _ _ disp_id_pstrans_data.
proof: Proof. apply is_disp_pstrans_from_total. pose (PP := id_pstrans (total_psfunctor _ _ _ FF)). pose (PP2 := pstrans_to_is_pstrans PP). assert (pr11 PP = total_pstrans_data FF FF (id_pstrans F) disp_id_pstrans_data). - use total2_paths_f. + apply idpath. + apply funextsec. intro x. apply funextsec. intro y. apply funextsec. intro f. use subtypePath. { intro. apply isaprop_is_invertible_2cell. } apply idpath. - exact (transportf _ X PP2). Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Constructions UniMath.Bicategories.Core.Bicat UniMath.Bicategories.Core.Examples.Initial UniMath.Bicategories.Core.Examples.Final UniMath.Bicategories.DisplayedBicats.DispBicat UniMath.Bicategories.Core.Univalence UniMath.Bicategories.Core.Invertible_2cells UniMath.Bicategories.DisplayedBicats.DispInvertibles UniMath.Bicategories.DisplayedBicats.DispAdjunctions UniMath.Bicategories.DisplayedBicats.DispUnivalence UniMath.Bicategories.PseudoFunctors.Display.PseudoFunctorBicat UniMath.Bicategories.PseudoFunctors.PseudoFunctor UniMath.Bicategories.PseudoFunctors.Examples.Identity UniMath.Bicategories.PseudoFunctors.Examples.Composition UniMath.Bicategories.Transformations.PseudoTransformation UniMath.Bicategories.Transformations.Examples.Whiskering UniMath.Bicategories.Transformations.Examples.Unitality UniMath.Bicategories.Transformations.Examples.Associativity UniMath.Bicategories.DisplayedBicats.DispPseudofunctor