Definition st_ok_for_col st interp :=
  @st_ok Tarski_is_a_Arity_for_col
         Tarski_is_a_Coinc_predicates_for_col st interp.

Lemma collect_wds_for_col : forall A B pa pb st interp, A <> B -> interp pa = A -> interp pb = B -> st_ok_for_col st interp -> st_ok_for_col (STadd (pa, pb) st) interp.