proposition: Lemma inhabited_set_nonempty: forall U (S: Ensemble U) v, S v -> Same_set S (Empty_set U) -> False.
proof: Proof. intros. assert (Ensembles.Inhabited _ S). { apply (Ensembles.Inhabited_intro _ _ v); trivial. } apply (Constructive_sets.Inhabited_not_empty _ _ H1). apply Ensembles.Extensionality_Ensembles; trivial. Qed.
imports: CertiGraph.lib.Coqlib CertiGraph.lib.EquivDec_ext CertiGraph.lib.List_ext CertiGraph.lib.Ensembles_ext CertiGraph.lib.EnumEnsembles CertiGraph.graph.graph_model CertiGraph.graph.path_lemmas CertiGraph.graph.graph_gen CertiGraph.graph.MathGraph CertiGraph.graph.LstGraph CertiGraph.graph.FiniteGraph CertiGraph.graph.reachable_computable