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.