proposition: Lemma connected_graph_zig_zag_strong_induction_symmetric {g : graph} (x : vertex g) {y : vertex g} (H : is_connected g) (P : vertex g -> UU) (Hsymm : ∏ [a b : vertex g], edge b a -> (edge a b -> P b) -> P b) : (P x) -> (∏ (a b : vertex g), P a -> edge a b -> P b) -> P y.
proof: Proof. intros Px IHn. apply (connected_graph_zig_zag_strong_induction x H P Px). intros a b Pa e. destruct e. - apply (IHn a b Pa e). - apply (Hsymm a b e). intro e'. apply (IHn a b Pa e'). 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