proposition: Lemma disp_functor_eq {C C':category} {F: functor C C'} {D:disp_cat C} {D':disp_cat C'} (DF DF': disp_functor F D D') : pr1 DF = pr1 DF' -> DF = DF'.
proof: Proof. intro H. apply (total2_paths_f H). apply proofirrelevance. apply isaprop_disp_functor_axioms. Defined.
imports: UniMath.Foundations.Sets UniMath.MoreFoundations.PartA UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Isos