proposition: Lemma eq_discrete_fib_mor (F G : precat_of_discrete_fibs_ob_mor) (a b : F --> G) (H : ∏ x y, pr1 (pr1 a) x y = pr1 (pr1 b) x y) : a = b.
proof: Proof. apply subtypePath. { intro. apply isaprop_disp_functor_axioms. } use total2_paths_f. - apply funextsec. intro x. apply funextsec. intro y. apply H. - repeat (apply funextsec; intro). apply disp_mor_unique_disc_fib. Qed.
imports: UniMath.Foundations.Sets UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Categories.HSET.Core UniMath.CategoryTheory.Categories.HSET.MonoEpiIso UniMath.CategoryTheory.Categories.HSET.Univalence UniMath.CategoryTheory.Limits.Pullbacks UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.Equivalences.Core UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.opp_precat UniMath.CategoryTheory.Presheaf UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Functors UniMath.CategoryTheory.DisplayedCats.NaturalTransformations UniMath.CategoryTheory.DisplayedCats.Fiber UniMath.CategoryTheory.DisplayedCats.Isos UniMath.CategoryTheory.DisplayedCats.Univalence UniMath.CategoryTheory.DisplayedCats.Examples.Opposite