proposition: Lemma add_edge_graph (G : pre_graph) (graph_G : is_graph G) x y u : x \in vset G -> y \in vset G -> is_graph (add_edge G x u y).
proof: Proof. exact: add_edge_graph'. 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)