proposition: Lemma reachable_acyclic: forall (g: Gph) n1 P n2, g |= n1 ~o~> n2 satisfying P <-> g |= n1 ~~> n2 satisfying P.
proof: Proof. split; intros. destruct H as [p [? ?]]. apply (good_path_acyclic g P p n1 n2 H) in H0. destruct H0 as [p' [? ?]]. exists p'. destruct H1. split; auto. split; auto. destruct H as [p [? ?]]. exists p. trivial. 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