proposition: Lemma graph_zig_zag_strong_induction {g : graph} {x y : vertex g} (gs : graph_zig_zag x y) : ∏ (P : vertex g -> UU), (P x) -> (∏ (a b : vertex g), P a -> (edge a b ⨿ edge b a) -> P b) -> P y.
proof: Proof. intros P Hx Hind. destruct gs as [n gs]. use graph_zig_zag_strong_induction_helper. - exact n. - exact x. - exact Hx. - exact Hind. - exact gs. 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