Definition ss_ok_for_cop ss interp :=
  @ss_ok Tarski_is_a_Arity_for_cop
         Tarski_is_a_Coinc_predicates_for_cop ss interp.

Lemma collect_coincs_for_cop : forall A B C D pa pb pc pd ss interp, Coplanar A B C D -> interp pa = A -> interp pb = B -> interp pc = C -> interp pd = D -> ss_ok_for_cop ss interp -> ss_ok_for_cop (SS.add (@CPToSS 4 (pa, (pb, (pc, pd)))) ss) interp.