intuition.
unfold O1_count in *.
fcf_simp_in_support.
destruct x.
fcf_simp_in_support.
trivial.
Qed.

Theorem Oi_count_increases :
forall i d1 b1 c1 a2 b2 c2,
In (d1, (b1, c1)) (getSupport (Oi i (b2, c2) a2)) ->
c1 = S c2.