proposition: Lemma edgesP (G : sgraph) (e : {set G}) : reflect (exists x y, e = [set x;y] /\ x -- y) (e \in E(G)).
proof: Proof. apply: (iffP imset2P) => [[x y]|[x] [y] [E xy]]. - rewrite !inE /= => _ xy ->. by exists x; exists y. - exists x y => //. by rewrite inE. Qed.
imports: Coq(Setoid CMorphisms) mathcomp(all_ssreflect) GraphTheory(edone preliminaries bij digraph) GraphTheory(set_tac)