Definition sf_SF_val_fun (f : R -> R) (a b : R) (n : nat) : StepFun a b.

Lemma SF_val_fun_rw (f : R -> R) (a b : R) (n : nat) (x : R) (Hx : a <= x <= b) : SF_val_fun f a b n x = match (unif_part_nat a b n x Hx) with | inleft H => f (a + (INR (proj1_sig H) + /2) * (b-a) / (INR n + 1)) | inright _ => f (a + (INR n + /2) * (b-a) / (INR n + 1)) end.