proposition: Lemma guarded_bij_proper_aux2: forall PV PE vmap1 vmap2 emap1 emap2 (G: PreGraph V E) (G': PreGraph V' E'), guarded_pointwise_relation PV eq vmap1 vmap2 -> guarded_pointwise_relation PE eq emap1 emap2 -> guarded_bij PV PE vmap1 emap1 G G' -> guarded_bij PV PE vmap2 emap2 G G'.
proof: Proof. intros. split; intros. + rewrite <- H. apply (vmap_inj H1); auto. + rewrite <- H0. apply (emap_inj H1); auto. + eapply guarded_morphism_proper_aux2; eauto. apply bij_is_morphism; auto. Qed.
imports: CertiGraph.lib.Coqlib CertiGraph.lib.Ensembles_ext CertiGraph.lib.EquivDec_ext CertiGraph.lib.relation_list CertiGraph.lib.Morphisms_ext CertiGraph.lib.List_ext CertiGraph.graph.graph_model CertiGraph.graph.path_lemmas CertiGraph.graph.reachable_ind CertiGraph.graph.subgraph2 CertiGraph.graph.graph_gen CertiGraph.graph.graph_relation