(** ** SF_sorted *)
Definition SF_sorted (Ord : R -> R -> Prop) (s : SF_seq) :=
sorted Ord (SF_lx s).
End SF_seq.
(** ** SF_map *)
Section SF_map.
Context {T T0 : Type}.
Definition SF_map  (f : T -> T0) (s : SF_seq) : SF_seq :=
mkSF_seq (SF_h s) (map (fun x => (fst x,f (snd x))) (SF_t s)).

Lemma SF_map_ly (f : T -> T0) (s : SF_seq) :
SF_ly (SF_map f s) = map f (SF_ly s).