End SetLems.
(* lemmas about interpreting clausesets *)
Section SetDenoteLems.
Context (B : Type). Variables (f : clause -> pred B) (b : pred B).
Variable (h : M.t -> clause -> M.t).
Variable (H : forall c cls s, setd f inter b cls s -> f c s ->
setd f inter b (h cls c) s).

Lemma setd_fold_left cls0 l s :
listd f inter b l s -> setd f inter b cls0 s ->
setd f inter b (fold_left h l cls0) s.