proposition: Proposition comp_functor_counit_laws : is_nat_trans _ _ comp_functor_counit_data.
proof: Proof. intros g₁ g₂ h. use eq_mor_cod_fib. cbn -[fiber_category]. rewrite !comp_in_cod_fib. cbn. etrans. { apply (PullbackArrow_PullbackPr1 (HC y (pr1 g₂) x (pr2 g₂) f)). } rewrite transportf_cod_disp. cbn. apply idpath. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Prelude UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.Limits.Pullbacks UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Isos UniMath.CategoryTheory.DisplayedCats.Fiber UniMath.CategoryTheory.DisplayedCats.Fibrations UniMath.CategoryTheory.DisplayedCats.Codomain UniMath.CategoryTheory.DisplayedCats.Codomain.FiberCod UniMath.CategoryTheory.DisplayedCats.DependentSums