Definition graph_zig_zag_of_length {g : graph} (n : nat) : ∏ (x y : vertex g), UU. Proof. induction n as [ | n IHn ]. - exact (λ x y, x = y). - exact (λ x y, ∑ (z : vertex g), ((edge x z) ⨿ (edge z x)) × IHn z y). Defined.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.MoreFoundations.Propositions. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.Adjunctions.Core.