Proposition finlim_dfl_comp_cat_unit_laws : is_pstrans finlim_dfl_comp_cat_unit_data. Proof. refine (_ ,, _ ,, _). - refine (λ (C₁ C₂ : univ_cat_with_finlim) (F G : functor_finlim C₁ C₂) (τ : nat_trans_finlim F G), _). use nat_trans_finlim_eq. intro x ; cbn. rewrite id_right, id_left. apply idpath. - refine (λ (C : univ_cat_with_finlim), _). Opaque comp_psfunctor. use nat_trans_finlim_eq. Transparent comp_psfunctor. intro x ; cbn. rewrite !id_left. apply idpath. - refine (λ (C₁ C₂ C₃ : univ_cat_with_finlim) (F : functor_finlim C₁ C₂) (G : functor_finlim C₂ C₃), _). Opaque comp_psfunctor. use nat_trans_finlim_eq. Transparent comp_psfunctor. intro x ; cbn. rewrite !id_left, !id_right. exact (!(functor_id _ _)). Opaque comp_psfunctor. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Equivalences.Core. Require Import UniMath.CategoryTheory.Limits.Preservation. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Core.Examples.StructuredCategories. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.PseudoFunctors.Display.PseudoFunctorBicat. Require Import UniMath.Bicategories.PseudoFunctors.PseudoFunctor. Require Import UniMath.Bicategories.PseudoFunctors.Examples.Identity. Require Import UniMath.Bicategories.PseudoFunctors.Examples.Composition. Require Import UniMath.Bicategories.Transformations.PseudoTransformation. Require Import UniMath.Bicategories.ComprehensionCat.BicatOfCompCat. Require Import UniMath.Bicategories.ComprehensionCat.DFLCompCat. Require Import UniMath.Bicategories.ComprehensionCat.Biequivalence.FinLimToDFLCompCat. Require Import UniMath.Bicategories.ComprehensionCat.Biequivalence.DFLCompCatToFinLim.