proposition: Lemma edges_opn0 (G : sgraph) (x : G) : E(G) = set0 -> #|N(x)| = 0.
proof: Proof. move => E0; apply: eq_card0 => y; rewrite !inE; apply: contra_eqF E0 => xy. by apply/set0Pn; exists [set x;y]; rewrite in_edges. Qed.
imports: Coq(Setoid CMorphisms) mathcomp(all_ssreflect) GraphTheory(edone preliminaries bij digraph) GraphTheory(set_tac)