proposition: Lemma edges_at_added_vertex (G : pre_graph) (isG : is_graph G) x a : x \notin vset G -> edges_at (G ∔ [x, a]) x = fset0.
proof: Proof. move => Hx. apply/fsetP => e. rewrite inE edges_atE. case Ee : (_ \in _) => //=. rewrite incident_addv. apply: contraNF Hx. exact: incident_vset. 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)