proposition: Lemma oiso2_remove_vertexE (F G : pre_graph) (z : VT) (j : F ⩭2 G) A B x : x \in vset (F \ z) -> @oiso2_remove_vertex F G z j A B x = j x.
proof: Proof. case: j => isF isG j Vx. rewrite /= !vfun_bodyE fsetD_bijE. - rewrite !inE [_ \in vset G]valP andbT. rewrite vfun_bodyE val_eqE bij_eqLR bijK. by case/fsetD1P : (Vx). - move => p. by rewrite /= (vfun_bodyE _ (fsetDl Vx)). 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)