Definition ss_ok_for_col ss interp :=
  @ss_ok Tarski_is_a_Arity_for_col
         Tarski_is_a_Coinc_predicates_for_col ss interp.

Lemma collect_coincs_for_col : forall A B C pa pb pc ss interp, Col A B C -> interp pa = A -> interp pb = B -> interp pc = C -> ss_ok_for_col ss interp -> ss_ok_for_col (SS.add (@CPToSS 3 (pa, (pb, pc))) ss) interp.