Definition SF_val_seq {T} (f : R -> T) (a b : R) (n : nat) : SF_seq :=
SF_seq_f2 (fun x y => f ((x+y)/2)) (unif_part a b n).
Definition SF_val_fun {T} (f : R -> T) (a b : R) (n : nat) (x : R) : T :=
SF_fun_f2 (fun x y => f ((x+y)/2)) (unif_part a b n) x.
Definition SF_val_ly {T} (f : R -> T) (a b : R) (n : nat) : seq T :=
behead (pairmap (fun x y => f ((x+y)/2)) 0 (unif_part a b n)).

(* Specifications: *)
Lemma SF_val_ly_bound {T} (f : R -> T) (a b : R) (n : nat) :
SF_val_ly f a b n = rev (SF_val_ly f b a n).