Proof with auto.
intro A; apply listd_In_pred; [|auto]; intros a C.
apply listd_In_inv_pred with (l := M.elements cls)...
apply setd_rem_In_inv_elems with (x := c)...
Qed.

(* Specifications: *)
Lemma setd_empty_set s : setd f inter TT M.empty s.
Lemma setd_filter bf cls s :
setd f inter TT cls s -> setd f inter TT (M.filter bf cls) s.