proposition: Lemma is_partial_lgraph_connected: forall (g1 g2: LGraph), is_partial_lgraph g1 g2 -> forall u v, connected g1 u v -> connected g2 u v.
proof: Proof. intros. destruct H0 as [p ?]. destruct H0. exists p. split. apply (is_partial_lgraph_valid_upath g1 g2); auto. auto. Qed.
imports: Coq.Logic.Classical CertiGraph.lib.List_ext CertiGraph.lib.EquivDec_ext CertiGraph.graph.graph_model CertiGraph.graph.graph_relation CertiGraph.graph.path_lemmas CertiGraph.graph.graph_gen CertiGraph.graph.FiniteGraph