Definition internal_sfib_to_rep_internal_sfib (H : internal_sfib) : rep_internal_sfib. Proof. split. - intros x f g α. pose (lift := pr1 H x g f α). exact (pr1 lift ,, (pr12 lift ,, inv2cell_to_z_iso (pr122 lift)) ,, pr2 (pr222 lift) ,, pr1 (pr222 lift)). - exact (pr2 H). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.StreetFibration. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.Univalence.