proposition: Lemma si_partialgraph_stronger_trans: forall (g1 g g2: PreGraph V E) (P1 P2 P: V -> Prop), Included P P1 -> Included P P2 -> (predicate_partialgraph g1 P1) ~=~ (predicate_partialgraph g P1) -> (predicate_partialgraph g P2) ~=~ (predicate_partialgraph g2 P2) -> (predicate_partialgraph g1 P) ~=~ (predicate_partialgraph g2 P).
proof: Proof. intros. transitivity (predicate_partialgraph g P). + apply si_stronger_partialgraph_simple with P1; auto. + apply si_stronger_partialgraph_simple with P2; auto. Qed.
imports: Coq.Logic.ProofIrrelevance Coq.Sets.Ensembles Coq.Sets.Finite_sets Coq.Classes.Morphisms CertiGraph.lib.Coqlib CertiGraph.lib.Ensembles_ext CertiGraph.lib.relation_list CertiGraph.lib.List_ext CertiGraph.lib.Equivalence_ext CertiGraph.lib.EquivDec_ext VST.msl.Coqlib2 Coq.Lists.List CertiGraph.graph.graph_model CertiGraph.graph.path_lemmas CertiGraph.graph.reachable_ind