Section CoincR_for_concyclic.
Context `{TE:Tarski_euclidean}.
Definition ss_ok_for_concy ss interp :=
@ss_ok Tarski_is_a_Arity_for_concy
Tarski_is_a_Coinc_predicates_for_concy ss interp.
Definition st_ok_for_concy st interp :=
@st_ok Tarski_is_a_Arity_for_concy
Tarski_is_a_Coinc_predicates_for_concy st interp.
Definition test_coinc_for_concy ss st (pa pb pc pd : positive) :=
@test_coinc Tarski_is_a_Arity_for_concy ss st (pa, (pb, (pc, pd))).
Definition interp_CP_for_concy (pa pb pc pd : positive) interp :=
@interp_CP Tarski_is_a_Arity_for_concy 3 (pa, (pb, (pc, pd))) interp.

Lemma test_coinc_ok_for_concy : forall pa pb pc pd ss st interp,
ss_ok_for_concy ss interp ->
st_ok_for_concy st interp ->
test_coinc_for_concy ss st pa pb pc pd = true ->
Concyclic_gen (interp pa) (interp pb) (interp pc) (interp pd).