Suppose $$

A

is a Boolean formula. Let $()$

c

$($

A

$)$

denote the complexity of $$

A

and $()$

s

$($

A

$)$

denote the number of subformuals of $$

A

$.$ Prove using the induction on the complexity of the formula $$

A

that $()<=2()+1$

s

$($

A

$)$

$<=$

$2$

c

$($

A

$)$

$+$

$1$

$.$