proposition: Lemma flip_edgeK (G : pre_graph) (e : ET) (x : VT) : e \in edges_at G x -> (flip_edge G e) \ x ≡G G \ x.
proof: Proof. move => He. split; rewrite //= edges_at_flip_edge //. - move => b e' /fsetDP [A B]. rewrite updateE //. by apply: contraNneq B => ->. - move => e' /fsetDP [A B]. rewrite updateE //. by apply: contraNneq B => ->. 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)