Theorem O1_count_Oi_eq_until_bad : forall s s_A, comp_spec (fun a b => ((snd (snd a) > q) <-> (snd (snd b) > q)) /\ ((snd (snd a) <= q)%nat -> (fst a = fst b /\ fst (snd a) = fst (snd b)))) ((A1 s_A) _ _ O1_count (s, 0)%nat) ((A1 s_A) _ _ (Oi q) (s, 0)%nat).