proposition: Lemma is_edge_flip_edge (G : pre_graph) e1 e2 x y u : e2 != e1 -> is_edge G e2 x u y -> is_edge (flip_edge G e1) e2 x u y.
proof: Proof. move => D. by rewrite /is_edge /flip_edge /= !updateE. Qed.
imports: HB(structures) Coq(Relation_Definitions Morphisms RelationClasses) mathcomp(all_ssreflect) GraphTheory(edone finite_quotient preliminaries bij equiv) GraphTheory(setoid_bigop structures pttdom rewriting) GraphTheory(finmap_plus)