proposition: Lemma graph_to_tree_contains_all_edges: forall lim root s d (H: Enumerable Vertex (reachable G root)), vvalid G root -> is_tree G root -> reachable G root s -> reachable G root d -> G |= s ~> d -> 2 * sizeOfEnum H - 1 <= lim -> graph_match_tree_edges s d (snd (graph_to_tree lim root)).
proof: Proof. intros. apply ((proj1 (graph_to_tree_contains_all_edges' lim _ _ _ H0 H1 H2 H3 H4)) H H5). Qed.
imports: Coq.Arith.Arith CertiGraph.lib.Coqlib CertiGraph.lib.EnumEnsembles CertiGraph.lib.EquivDec_ext CertiGraph.lib.List_ext CertiGraph.graph.graph_model CertiGraph.graph.path_lemmas CertiGraph.graph.subgraph2 CertiGraph.graph.MathGraph CertiGraph.graph.FiniteGraph CertiGraph.graph.reachable_computable Coq.Lists.List