proposition: Lemma step_reachable_by: forall (g: Gph) n1 n2 n3 (P: Ensemble V), vvalid g n1 -> P n1 -> step g n1 n2 -> g |= n2 ~o~> n3 satisfying P -> g |= n1 ~o~> n3 satisfying P.
proof: Proof. intros. eapply edge_reachable_by; eauto. split; [| split]; auto. apply reachable_by_head_valid in H2; 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