Proof with auto with real.
intros.
repeat rewrite <- Rplus_assoc.
rewrite Rplus_0_r.
rewrite plus_comm.
replace
(2 * / INR (S (j - i)) * INR (i - b) + 1 + 1 + 2 * / INR (S (j - i)) * INR (n + b - j)) with
(2 * / INR (S (j - i)) * (INR (i - b) + INR (n + b - j)) + 2).
rewrite <- plus_INR.
replace ((i - b + (n + b - j))%nat) with ((S n - S (j - i))%nat) by omega.
rewrite minus_INR.
field.
split...
omega.
field...
Qed.

Lemma Index_In_dec (i: Index ee ol) l: { In i l } + { ~ In i l }.