proposition: Lemma expand_isolated (G : pre_graph) (z : VT) (isG : is_graph G) (isH : is_graph (G \ z)) : z \in vset G -> edges_at G z = fset0 -> pack G ≃2 pack (G \ z) ∔ lv G z.
proof: Proof. move => Vz Iz. symmetry. apply: iso2_comp (iso2_sym _) _. apply: pack_add_vertex. instantiate (1 := z). - by rewrite !inE eqxx. - apply: eqvG_pack. by rewrite remove_vertexK // Iz remove_edges0. 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)