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

Lemma identify_lines_ok : forall ss sp interp,
ss_ok ss interp -> sp_ok sp interp ->
ss_ok (identify_lines ss sp) interp.