intuition.
unfold Oi.
fcf_well_formed.
destruct (ge_dec b0 i); fcf_well_formed.
Qed.

(* We will need to know that the count increases by one after each call to O1_count and Oi. *)
Theorem O1_count_increases :
forall d1 b1 c1 a2 b2 c2,
In (d1, (b1, c1)) (getSupport (O1_count (b2, c2) a2)) ->
c1 = S c2.