proposition: Lemma spanning_preserves_vertices: forall g t v, spanning t g -> (vvalid g v <-> vvalid t v).
proof: Proof. intros; split; intros; pose proof (connected_refl _ v H0); apply H in H1; apply connected_vvalid in H1; apply H1. 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