proposition: Lemma catiso_is_globally_prop (x : C) : ∏ d1 d2 : D x, d1 = d2.
proof: Proof. intros d1 d2. set (h := total2_section_path x d2 (λ z, invweq (object_as_proj_equal_fibers z) (pr2 (inv_i z)))). refine (_ @ h (catiso_is_globally_prop' x _ d2)). set (h' := total2_section_path x d1 (λ z, invweq (object_as_proj_equal_fibers z) (pr2 (inv_i z)))). exact (! h' (catiso_is_globally_prop' x _ d1)). Defined.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.catiso UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Isos UniMath.CategoryTheory.DisplayedCats.Total UniMath.CategoryTheory.DisplayedCats.Univalence