proposition: Lemma In_partition_unmatched {A} : forall f (l : list A) a, List.In a (snd (List.partition f l)) -> f a = false.
proof: Proof. induction l; simpl; intros; intuition; simpl; subst; eauto. case_eq (f a); destruct (List.partition f l); simpl; intuition; rewrite H0 in H; eauto; inversion H; subst; eauto. 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