proposition: Lemma adjacent_connected: forall g u v, adjacent g u v -> connected g u v.
proof: Proof. intros. exists (u::v::nil). split. split. auto. simpl. destruct H. destruct H. destruct H. destruct H0; destruct H0. rewrite <- H2; apply H1. rewrite <- H0; apply H1. split; simpl; 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