proposition: Lemma exists_in_list {A} : forall (xs : list A) x, (exists n, nth_error xs n = Some x) -> List.In x xs.
proof: Proof. intros. revert x H. induction xs; intros. - destruct H. destruct x0; inversion H. - simpl in *. destruct H. destruct x0. * left. inversion H. auto. * right. apply IHxs. eexists. apply H. Qed.
imports: Fiat.Common.Coq__8_4__8_5__Compat Coq.ZArith.ZArith Coq.Lists.List Coq.Lists.SetoidList Coq.Bool.Bool Fiat.Common Fiat.Common.List.Operations Fiat.Common.Equality Fiat.Common.List.FlattenList Fiat.Common.LogicFacts