proposition: Lemma si_stronger_partialgraph': forall (g1 g2: PreGraph V E) (p1 p2 p1' p2' p: V -> Prop), Same_set p1' (Intersection _ p1 p) -> Same_set p2' (Intersection _ p2 p) -> (predicate_partialgraph g1 p1) ~=~ (predicate_partialgraph g2 p2) -> (predicate_partialgraph g1 p1') ~=~ (predicate_partialgraph g2 p2').
proof: Proof. intros. apply si_stronger_partialgraph with (p := p) (p1 := p1) (p2 := p2); auto. - intros. rewrite Same_set_spec in H; specialize (H v). rewrite Intersection_spec in H; auto. - intros. rewrite Same_set_spec in H0; specialize (H0 v). rewrite Intersection_spec in H0; 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