proposition: Lemma add_edge_remove_vertex (G : pre_graph) e x u y : e \notin eset G -> G ∔ [e,x,u,y] \ y ≡G G \ y.
proof: Proof. move => He. split => //=; rewrite edges_at_add_edge. 2: move => b. all: rewrite fsetUDU ?fdisjoint1X // => f /fsetDP [Hf _]; rewrite update_neq //; by apply: contraNneq He => <-. 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)