Section FoldLemWeak.
Context (B : Type). Variables (f : clause -> pred B) (b : pred B).
Variable (h : list clause -> clause -> list clause).
Variable (H : forall c cls s, listd f inter b cls s -> (forall s, f c s) ->
listd f inter b (h cls c) s).
Proof with simpl; auto.
revert cls0 s; induction l... intros s0 s H1.
assert (H2: forall s, f a s). intros s'. destruct H1 as [H1 H2]. spec H1 s'...
intros D; apply IHl... destruct H1...
Qed.
End FoldLemWeak.

Lemma setd_filter_pred:
forall {B: Type} (f: M.elt -> pred B) (h: M.elt -> bool) (s: M.t),
setd f inter TT s |-- setd f inter TT (M.filter h s).