Definition fibration_is_street_fib (HD : cleaving D) : street_fib (pr1_category D). Proof. intros e b f. pose (HD (pr1 e) b f (pr2 e)) as c. refine ((b ,, pr1 c) ,, ((f ,, pr12 c) ,, identity_z_iso b) ,, _). simpl. split. - apply (!(id_left _)). - apply is_cartesian_to_is_cartesian_sfib. exact (pr22 c). 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.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.CategoryTheory.DisplayedCats.Fibrations.