Section CoincR_for_cop.
Context `{TnEQD:Tarski_neutral_dimensionless_with_decidable_point_equality}.
Definition ss_ok_for_cop ss interp :=
@ss_ok Tarski_is_a_Arity_for_cop
Tarski_is_a_Coinc_predicates_for_cop ss interp.
Definition st_ok_for_cop st interp :=
@st_ok Tarski_is_a_Arity_for_cop
Tarski_is_a_Coinc_predicates_for_cop st interp.
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).