Definition sp_ok (sp : SP.t) (interp: positive -> COLTpoint) :=
forall p, SP.mem p sp = true -> interp (fstpp p) <> interp (sndpp p).

Lemma test_col_ok : forall ss sp interp p1 p2 p3,
ss_ok ss interp -> sp_ok sp interp ->
test_col ss sp p1 p2 p3 = true ->
CTCol (interp p1) (interp p2) (interp p3).