proposition: Lemma nil_in_false : forall {A} seq, seq = nil <-> ~ exists (x: A), List.In x seq.
proof: Proof. split; intro H. intros [ x in_seq ]; subst; eauto using in_nil. destruct seq as [ | a ]; trivial. exfalso; apply H; exists a; simpl; intuition. 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