proposition: Lemma path_prop_weaken: forall g (P1 P2 : Ensemble V) p, (forall d, P1 d -> P2 d) -> path_prop g P1 p -> path_prop g P2 p.
proof: Proof. intros; hnf in *; intros; hnf in *; destruct p. simpl in *. destruct H0. split. - apply H; auto. - eapply Forall_impl; eauto. simpl. intuition. 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