proposition: Lemma graph_match_tree_edges_cons_1: forall s d root t tL, graph_match_tree_edges s d (T root (t :: nil)) -> graph_match_tree_edges s d (T root (t :: tL)).
proof: Proof. intros. destruct H as [t' [? ?]]. inversion H; subst. + exists (T root (t :: tL)). split. 1: apply FT_base. simpl in *. destruct t. 1: inversion H0. destruct H0. 2: exfalso; auto. subst. apply in_eq. + exists t'. split; auto. apply FT_succ with tr'; auto. simpl in *. destruct H4. 2: exfalso; auto. left; auto. 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