proposition: Lemma faithful_pr1_category {C : category} (D : disp_cat C) (H : ∏ (a b : total_precategory D) (x : C ⟦ pr1 a, pr1 b ⟧), isaprop (pr2 a -->[ x] pr2 b)) : faithful (pr1_category D).
proof: Proof. intros ? ?. apply isinclpr1, H. Defined.
imports: UniMath.Foundations.Sets UniMath.MoreFoundations.AxiomOfChoice UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Functors UniMath.CategoryTheory.DisplayedCats.NaturalTransformations UniMath.CategoryTheory.DisplayedCats.Isos UniMath.CategoryTheory.DisplayedCats.Univalence