proposition: Lemma edges_eqn_sub (G : sgraph) (e1 e2 : {set G}) : e1 \in E(G) -> e2 \in E(G) -> e1 != e2 -> ~~ (e1 \subset e2).
proof: Proof. move => /edgesP [x1 [y1 [-> xy1]]] /edgesP [x2 [y2 [-> xy2]]]. apply/contraNN; rewrite subUset !sub1set !inE => EQS. case/andP : EQS xy1 xy2 => /pred2P[->|->] /pred2P [->|->]. all: by rewrite ?sg_irrefl // setUC. Qed.
imports: Coq(Setoid CMorphisms) mathcomp(all_ssreflect) GraphTheory(edone preliminaries bij digraph) GraphTheory(set_tac)