fact: Definition pick_lengths_aux (s1 : SSP.elt) (ss : SSP.t) : (option (SSP.elt * SSP.elt)) := match (exists_witness (fun s2 => negb (SP.is_empty (SP.inter s1 s2))) ss) with | None => None | Some s2 => Some(s1,s2) end.
imports: Recdef NArith GeoCoq.Utils.sets