proposition: Lemma trafotarget_disp_cat_id_comp: disp_cat_id_comp C trafotarget_disp_cat_ob_mor.
proof: Proof. split. - intros c α. red. unfold trafotarget_disp_cat_ob_mor, make_disp_cat_ob_mor. hnf. do 2 rewrite functor_id. rewrite id_left. apply id_right. - intros c1 c2 c3 f g α1 α2 α3 Hypf Hypg. red. red in Hypf, Hypg. unfold trafotarget_disp_cat_ob_mor, make_disp_cat_ob_mor in Hypf, Hypg |- *. hnf in Hypf, Hypg |- *. do 2 rewrite functor_comp. rewrite assoc. rewrite Hypf. rewrite <- assoc. rewrite Hypg. apply assoc. Qed.
imports: UniMath.Foundations.PartD UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.HorizontalComposition UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Total UniMath.CategoryTheory.DisplayedCats.Constructions UniMath.CategoryTheory.Monoidal.AlternativeDefinitions.MonoidalCategoriesTensored UniMath.CategoryTheory.Monoidal.AlternativeDefinitions.MonoidalFunctorsTensored UniMath.CategoryTheory.Monoidal.AlternativeDefinitions.DisplayedMonoidalTensored UniMath.Bicategories.MonoidalCategories.EndofunctorsMonoidal UniMath.Bicategories.MonoidalCategories.Actions UniMath.Bicategories.MonoidalCategories.ActionBasedStrength UniMath.Bicategories.MonoidalCategories.MonoidalFromBicategory UniMath.Bicategories.Core.Bicat UniMath.Bicategories.Core.BicategoryLaws UniMath.Bicategories.Core.Unitors UniMath.Bicategories.Core.Invertible_2cells UniMath.Bicategories.Core.Examples.BicatOfCats