proposition: Lemma mark1_inj: forall (g1 g2: Graph) (v: V), mark1 g1 v g2 <-> (g1 ~=~ g2 /\ SIMPLE_MARK_GRAPH.mark1 g1 (inj g1) v (inj g2)).
proof: Proof. intros. unfold mark1, SIMPLE_MARK_GRAPH.mark1. simpl. unfold marked. tauto. Qed.
imports: Coq.Logic.ProofIrrelevance CertiGraph.lib.Ensembles_ext Coq.Lists.List Coq.Classes.Morphisms CertiGraph.lib.Coqlib CertiGraph.lib.List_ext CertiGraph.lib.EquivDec_ext VST.msl.Coqlib2 CertiGraph.graph.graph_model CertiGraph.graph.path_lemmas CertiGraph.graph.reachable_computable CertiGraph.graph.reachable_ind CertiGraph.graph.graph_gen CertiGraph.graph.graph_relation CertiGraph.graph.subgraph2