proposition: Lemma in_not_nil : forall {A} x seq, @List.In A x seq -> seq <> nil.
proof: Proof. intros A x seq in_seq eq_nil. apply (@in_nil _ x). subst seq; assumption. 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