proposition: Lemma is_partial_lgraph_valid_upath: forall (g1 g2: LGraph) p, is_partial_lgraph g1 g2 -> valid_upath g1 p -> valid_upath g2 p.
proof: Proof. intros. induction p. auto. destruct p. simpl. simpl in H0. apply H. apply H0. destruct H0. split. apply (is_partial_lgraph_adjacent 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