Proof with try inversion 1; auto.
intro A. remember (M.min_elt cls) as b. destruct b...
eapply listd_In_inv_pred; eauto. solve[rewrite Heqb in H; eapply pick_In; eauto].
Qed.

Lemma setd_mem_add c cls cls' s :
clause_denote c s -> setd clause_denote inter TT cls s ->
mem_add c cls = Some cls' ->
setd clause_denote inter TT cls' s.