Lemma connected_graph_zig_zag_strong_induction {g : graph} (x : vertex g) {y : vertex g} (H : is_connected g) : ∏ (P : vertex g -> UU), (P x) -> (∏ (a b : vertex g), P a -> (edge a b ⨿ edge b a) -> P b) -> P y. Proof. apply graph_zig_zag_strong_induction. apply H. 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.