proposition: Lemma reachable_through_set_single: forall (g: Gph) x y, reachable_through_set g (x :: nil) y <-> reachable g x y.
proof: Proof. intros. unfold reachable_through_set; split; intros. + destruct H as [? [[? | ?] ?]]; [subst; auto |]. inversion H. + exists x; split; auto. left; auto. Qed.
imports: Coq.Logic.ProofIrrelevance Coq.micromega.Lia CertiGraph.lib.Coqlib CertiGraph.lib.EnumEnsembles CertiGraph.lib.List_ext CertiGraph.lib.EquivDec_ext CertiGraph.graph.graph_model Coq.Lists.List Coq.Lists.ListDec