proposition: Lemma isaprop_disp_cat_axioms (C : category) (D : disp_cat_data C) : isaprop (disp_cat_axioms C D).
proof: Proof. apply isofhlevelsn. intro X. set (XR := ( _ ,, X) : disp_cat C). apply isofhleveltotal2. - repeat (apply impred; intro). apply (@homsets_disp _ XR). - intros x. repeat (apply isofhleveldirprod); repeat (apply impred; intro). + apply (@homsets_disp _ XR). + apply (@homsets_disp _ XR). + apply isapropiscontr. Qed.
imports: UniMath.Foundations.Sets UniMath.Foundations.PartD UniMath.MoreFoundations.PartA UniMath.MoreFoundations.AxiomOfChoice UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.whiskering