proposition: 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: Proof. apply graph_zig_zag_strong_induction. apply H. Defined.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.MoreFoundations.Tactics UniMath.MoreFoundations.Propositions UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.Adjunctions.Core