$30$ marks$)$ The algorithm reverse$($lst$)$ below reverses a list in place. More precisely,

it satisfies the following precondition$/$postcondition pair:

Precondition: lst is an array of any length

Postcondition: lst upon completion of this algorithm, is mutated to the reversed

list. For example, if the list prior reversal is $[1,2,3],$ after the algorithm is completed,

the content of the list is $[3,2,1].$

functon reverse$($lst$)$:

n $=$ len$($lst$)$

i$,$ j $=0,$ n$-1$

while i $<=$ j:

swap$($lst$[$i$],$ lst$[$j$])$

i $=$ i $+1$

j $=$ j $-1$

Provide a complete proof of correctness of this algorithm performing all four

steps.