Definition locally_grpd_internal_sopfib {B : bicat} (HB : locally_groupoid B) {e b : B} (p : e --> b) : internal_sopfib p. Proof. split. - intros x f g α. refine (f ,, id2 _ ,, inv_of_invertible_2cell (make_invertible_2cell (HB _ _ _ _ α)) ,, locally_grpd_opcartesian HB _ _ ,, _). abstract (cbn ; rewrite id2_rwhisker ; rewrite vcomp_rinv ; apply idpath). - intro ; intros. apply (locally_grpd_opcartesian HB). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.Examples.OpCellBicat. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.UnivalenceOp. Require Import UniMath.Bicategories.Morphisms.InternalStreetFibration.