proposition: Lemma foot_none_nil {A}: forall (l : list A), foot l = None -> l = nil.
proof: Proof. induction l; intros; auto. simpl in H. destruct l. inversion H. specialize (IHl H). inversion IHl. Qed.
imports: Coq.Lists.List Coq.micromega.Lia Coq.Sorting.Permutation Coq.ZArith.ZArith_base Coq.ZArith.Zcomplements Coq.Logic.FunctionalExtensionality CertiGraph.lib.Coqlib CertiGraph.lib.EquivDec_ext VST.zlist.sublist VST.zlist.list_solver