proposition: Lemma step_list_partialgraph: forall (g: PreGraph V E) n l (P: Ensemble V), vvalid g n -> P n -> step_list g n l -> step_list (predicate_partialgraph g P) n l.
proof: Proof. intros. intro m; specialize (H1 m). rewrite H1; clear H1. split. + intros; apply partialgraph_step; auto. + intro. inv H1; simpl in *. econstructor. - destruct H2; eauto. - reflexivity. - reflexivity. Qed.
imports: Coq.Logic.ProofIrrelevance Coq.Sets.Ensembles Coq.Sets.Finite_sets Coq.Classes.Morphisms CertiGraph.lib.Coqlib CertiGraph.lib.Ensembles_ext CertiGraph.lib.relation_list CertiGraph.lib.List_ext CertiGraph.lib.Equivalence_ext CertiGraph.lib.EquivDec_ext VST.msl.Coqlib2 Coq.Lists.List CertiGraph.graph.graph_model CertiGraph.graph.path_lemmas CertiGraph.graph.reachable_ind