In questions $2$a through $2$d$,$ use a loop invariant to prove that LARGEST is correct. Your invariant, and your proof, may be written in mathematics, in English, or

in a mixture of the two.

$2$a$.(5$ points.$)$ Show a loop invariant for LARGEST. Hint: Your invariant may optionally use logical connectives like $-,{?}^{{?}^{?}},vv,,$ etc.

$2$b$.(5$ points.$)$ Prove that your invariant from $2a$ is true at initialization.

$2$c$.(10$ points.$)$ Prove that your invariant from $2a$ is true during maintenance.

$2$d$.(5$ points.$)$ Prove that your invariant from $2$a shows that LARGEST is correct at termination.