End SetDenoteLems.
Section FoldLem.
Context (B : Type). Variables (f : clause -> pred B) (b : pred B).
Variable (h : list clause -> clause -> list clause).

(* Specifications: *)
Lemma listd_fold_left cls0 l s
(H : forall c cls, listd f inter b cls s -> f c s ->
listd f inter b (h cls c) s) :
listd f inter b l s -> listd f inter b cls0 s ->
listd f inter b (fold_left h l cls0) s.