Definition eqopp (p1 p2 : option (SS.elt * SS.elt)) :=
match p1,p2 with
| None, None => True
| Some s1, Some s2 => True
| _, _ => False
end.

Lemma pick_varieties_ok_2 : forall s1 s2 ss st,
pick_varieties ss st = Some(s1,s2) ->
SS.In s2 (SS.remove s1 ss).