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

Lemma collect_cols :
forall (A B C : COLTpoint) (HCol : CTCol A B C) pa pb pc ss (interp :  positive -> COLTpoint),
interp pa = A ->
interp pb = B ->
interp pc = C ->
ss_ok ss interp -> ss_ok (SS.add (S.add pa (S.add pb (S.add pc S.empty))) ss) interp.