proposition: Lemma oiso2_incident (F G : pre_graph) (i : F ⩭2 G) (x : VT) (e : ET) : x \in vset F -> e \in eset F -> incident F x e = incident G (i x) (efun_of i e).
proof: Proof. move => Vx Ee. rewrite /incident. apply/existsP/existsP. - move => [b] e_x. exists (edir_of i e (+) b). rewrite oiso2_endpoint //. by rewrite addbA addbb [addb _ _]/= (eqP e_x). - move => [b] e_ix. exists (edir_of i e (+) b). rewrite oiso2_endpoint // in e_ix. move/eqP : e_ix. move/vfun_of_inj => -> //. rewrite -> endptP => //. exact: oiso2_graphL i. Qed.
imports: Coq(Relation_Definitions Morphisms RelationClasses) mathcomp(all_ssreflect) GraphTheory(edone finite_quotient preliminaries bij equiv) GraphTheory(setoid_bigop structures pttdom mgraph mgraph2) GraphTheory(rewriting open_confluence finmap_plus)