proposition: Lemma oarc_flip_edge (G : pre_graph) e1 e2 x y u : oarc G e2 x u y -> oarc (flip_edge G e1) e2 x u y.
proof: Proof. case: (altP (e2 =P e1)) => [->|D]. - case => E [b] [A B C]. split => //. exists (~~ b). rewrite /= !negbK !updateE. split => //. symmetry. rewrite eqvb_neq. symmetry. by rewrite cnvI. - case => E [b] [A B C]. split => //. exists b. by rewrite /= !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)