proposition: Lemma add_edge_graph' (G : pre_graph) (graph_G : is_graph G) e x y u : x \in vset G -> y \in vset G -> is_graph (G ∔ [e,x, u, y]).
proof: Proof. move => xG yG. split => //=; try apply graph_G. move => e' b; case/fset1UE => [->|[? ?]]; rewrite updateE ?(endptP) //. by case: b. 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)