Consider the following code fragment:

m $=1$;

q $=2$;

while$($m $$ n$)\{$

m $=$ m $+1$;

q $=$ q $*2$;

$\}$

Prove that this code fragment correctly computes q $=2$n if n $\{1,2,3,...\}.$ This is for practice. Prove it by the steps I used in the image.