proposition: Lemma foot_in {A}: forall (a : A) L, foot L = Some a -> In a L.
proof: Proof. induction L. inversion 1. icase L. simpl. inversion 1. auto. rewrite foot_simpl. right. auto. 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