proposition: Lemma reindexing_forward_id {c': C'} {x' : ob_disp reindexing_forward_ob_mor c'} : identity c' = double_transport (¤ x') (¤ x') (# F (identity (↙ x'))).
proof: Proof. destruct (¤ x'). apply pathsinv0. exact (functor_id_id C C' F _ _ (idpath _)). Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Functors UniMath.CategoryTheory.DisplayedCats.NaturalTransformations UniMath.CategoryTheory.DisplayedCats.Isos UniMath.CategoryTheory.DisplayedCats.Univalence UniMath.CategoryTheory.DisplayedCats.Fibrations UniMath.CategoryTheory.DisplayedCats.StreetFibration