proposition: Lemma uf_eq {c1 c2 : C} (f : C⟦c1,c2⟧) : ∏ (d1 : D c1) (d2 : D c2), (d1 -->[f] d2) ≃ (pr1 (uo c1) -->[f] pr1 (uo c2)).
proof: Proof. intros d1 d2. assert (p1 : d1 = pr1 (uo c1)). { apply uo. } assert (p2 : d2 = pr1 (uo c2)). { apply uo. } induction p1. induction p2. apply idweq. 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