proposition: Lemma reachable_by_head_prop: forall (g: Gph) n1 n2 P, g |= n1 ~o~> n2 satisfying P -> P n1.
proof: Proof. intros. destruct H as [p ?]. eapply reachable_by_path_In; eauto. apply reachable_by_path_head in H. destruct p as [v p]. simpl in H. subst. 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