Definition test_coinc_for_cop ss st (pa pb pc pd : positive) :=
  @test_coinc Tarski_is_a_Arity_for_cop ss st (pa, (pb, (pc, pd))).Definition interp_CP_for_cop (pa pb pc pd : positive) interp :=
  @interp_CP Tarski_is_a_Arity_for_cop 3 (pa, (pb, (pc, pd))) interp.

Lemma test_coinc_ok_for_cop : forall pa pb pc pd ss st interp, ss_ok_for_cop ss interp -> st_ok_for_cop st interp -> test_coinc_for_cop ss st pa pb pc pd = true -> Coplanar (interp pa) (interp pb) (interp pc) (interp pd).