Definition st_ok_for_cop st interp :=
  @st_ok Tarski_is_a_Arity_for_cop
         Tarski_is_a_Coinc_predicates_for_cop st interp.

Lemma collect_wds_for_cop : forall A B C pa pb pc st interp, ~ Col A B C -> interp pa = A -> interp pb = B -> interp pc = C -> st_ok_for_cop st interp -> st_ok_for_cop (STadd (pa, (pb, pc)) st) interp.