Definition postcomp_refl_comm {C : category} {D : disp_cat C} {c c' c'' c''' : C} {f : c' --> c} {f' : c'' --> c'} {g' : c''' --> c''} {d : D c} {d' : D c'} {d'' : D c''} {d''' : D c'''} (ff : d' -->[f] d) (ff' : d'' -->[f'] d') (gg' : d''' -->[g'] d'') (gg : d''' -->[g' · f'] d') (hh : d''' -->[g' · (f' · f)] d) (H : is_cartesian ff) (comm_right : gg ;; ff = transportf (mor_disp d''' d) (assoc g' f' f) hh) : (gg' ;; (ff' ;; ff) = hh) -> (gg' ;; ff' = gg).
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Categories.HSET.Core. Require Import UniMath.CategoryTheory.Categories.HSET.MonoEpiIso. Require Import UniMath.CategoryTheory.Categories.HSET.Univalence. Require Import UniMath.CategoryTheory.Limits.Pullbacks. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.Equivalences.Core. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.opp_precat. Require Import UniMath.CategoryTheory.Presheaf. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Constructions. Require Import UniMath.CategoryTheory.DisplayedCats.Fibrations. Require Import UniMath.CategoryTheory.DisplayedCats.MoreFibrations.Prefibrations.