proposition: Proposition cod_fiber_functor_on_eq {x y : C} {f g : x --> y} (p : f = g) (φ : C/y) : fiber_functor_on_eq HD p φ = cod_fiber_functor_on_eq_mor p φ.
proof: Proof. induction p. use eq_mor_cod_fib. use (MorphismsIntoPullbackEqual (isPullback_Pullback _)). - cbn. rewrite PullbackArrow_PullbackPr1. rewrite id_left. apply idpath. - cbn. rewrite PullbackArrow_PullbackPr2. rewrite id_left. apply idpath. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Prelude UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.Equivalences.Core UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.Limits.Pullbacks UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Fibrations UniMath.CategoryTheory.DisplayedCats.Fiber UniMath.CategoryTheory.DisplayedCats.Codomain