proposition: Lemma is_disp_modification_from_total (mm : disp_modification_data) : is_modification (total_modification_data mm) → is_disp_modification mm.
proof: Proof. intros Hmm. pose (Em := make_modification _ Hmm). intros x y f xx yy ff. pose (P := !fiber_paths (@modnaturality_of _ _ _ _ _ _ Em (x,,xx) (y,,yy) (f,,ff))). symmetry. etrans. { apply maponpaths. exact P. } unfold transportb. rewrite transport_f_f. rewrite transportf_set. * apply idpath. * apply B₂. 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.Modifications.Modification UniMath.Bicategories.DisplayedBicats.DispPseudofunctor UniMath.Bicategories.DisplayedBicats.DispTransformation