Section CoincR_for_col.
Context `{TnEQD:Tarski_neutral_dimensionless_with_decidable_point_equality}.
Definition ss_ok_for_col ss interp :=
@ss_ok Tarski_is_a_Arity_for_col
Tarski_is_a_Coinc_predicates_for_col ss interp.
Definition st_ok_for_col st interp :=
@st_ok Tarski_is_a_Arity_for_col
Tarski_is_a_Coinc_predicates_for_col st interp.
Definition test_coinc_for_col ss st (pa pb pc : positive) :=
@test_coinc Tarski_is_a_Arity_for_col ss st (pa, (pb, pc)).
Definition interp_CP_for_col (pa pb pc : positive) interp :=
@interp_CP Tarski_is_a_Arity_for_col 2 (pa, (pb, pc)) interp.

Lemma test_coinc_ok_for_col : forall pa pb pc ss st interp,
ss_ok_for_col ss interp ->
st_ok_for_col st interp ->
test_coinc_for_col ss st pa pb pc = true ->
Col (interp pa) (interp pb) (interp pc).