proposition: Lemma finite_graph_si: forall (g1 g2: PreGraph V E), g1 ~=~ g2 -> FiniteGraph g1 -> FiniteGraph g2.
proof: Proof. intros. destruct X as [X Y]. constructor. + revert X; apply Enumerable_Same_set. destruct H as [? _]; rewrite Same_set_spec; auto. + revert Y; apply Enumerable_Same_set. destruct H as [_ [? _]]; rewrite Same_set_spec; auto. Qed.
imports: CertiGraph.lib.Coqlib CertiGraph.lib.EnumEnsembles CertiGraph.lib.EquivDec_ext CertiGraph.lib.List_ext CertiGraph.lib.relation_list CertiGraph.lib.Equivalence_ext CertiGraph.graph.graph_model CertiGraph.graph.graph_gen CertiGraph.graph.path_lemmas