proposition: Lemma localDag_reachable_spec': forall g x S, vvalid g x -> localDag g x -> step_list g x S -> Prop_join (reachable_through_set g S) (eq x) (reachable g x).
proof: Proof. intros. destruct (localDag_reachable_spec _ _ _ H H0 H1). split. + intros y; specialize (H2 y). rewrite H2; clear. firstorder. + intros y; specialize (H3 y). firstorder. Qed.
imports: Coq.Logic.ProofIrrelevance Coq.Sets.Ensembles Coq.Sets.Finite_sets Coq.Lists.List Coq.Classes.Morphisms CertiGraph.lib.Coqlib CertiGraph.lib.List_ext CertiGraph.lib.EquivDec_ext VST.msl.Coqlib2 CertiGraph.graph.graph_model CertiGraph.graph.path_lemmas CertiGraph.graph.reachable_computable CertiGraph.graph.reachable_ind CertiGraph.graph.subgraph2