Proof with try solve [exfalso; auto]; auto.
induction l... simpl. intros [H1 H2]. if_tac... simpl... split...
Qed.

Lemma listd_partition_pred h l xs ys s (H : partition h l = (xs, ys)) :
listd f inter TT l s ->
listd f inter TT xs s /\ listd f inter TT ys s.