Fixpoint power (base : nat) (exp : nat) : nat :=
 match exp with
 | 0 => 1
 | S n => base * (power base n)
 end.

Lemma countBLeafCT_mono_lt: forall n1 n2 s, n1 < n2 -> 0 < countBLeafCT n1 s -> countBLeafCT n1 s < countBLeafCT n2 s .