Proof with try solve [exfalso; auto]; auto.
revert c0 H; induction l... simpl; intros c0 H C [D E]. apply H...
Qed.

(* Specifications: *)
Lemma listd_foldl_pred h c0 l s
(H : forall a x, f a s -> f x s -> f (h x a) s) :
f c0 s -> listd f inter TT l s -> f (fold_left h l c0) s.