Definition ss_ok (ss : SS.t) (interp: positive -> COLTpoint) :=
  forall s, SS.mem s ss = true ->
  forall p1 p2 p3, S.mem p1 s && S.mem p2 s && S.mem p3 s = true ->
    CTCol (interp p1) (interp p2) (interp p3).Definition sp_ok (sp : SP.t) (interp: positive -> COLTpoint) :=
  forall p, SP.mem p sp = true -> interp (fstpp p) <> interp (sndpp p).

Lemma collect_diffs : forall (A B : COLTpoint) (H : A <> B) pa pb sp (interp : positive -> COLTpoint), interp pa = A -> interp pb = B -> sp_ok sp interp -> sp_ok (SP.add (pa, pb) sp) interp.