The Following While Loop Is Annotated with a Pre- and Post-Condition

question 21

Essay

The following while loop is annotated with a pre- and post-condition and also a loop invariant.
Use the loop invariant theorem to prove the correctness of the loop with respect to the pre- and post-conditions.
$[$ Pre-condition: product $= A [ 1 ]$ and $i = 1 ]$ while $( i \neq m )$
1. $i : = i + 1$
2. product := product. $A [ i ]$
end while
$[$ Post-condition: product $= A [ 1 ] \cdot A [ 2 ] \cdots A [ m ] ]$
loop invariant: $I ( n )$ is $" i = n + 1$ and product $: = A [ 1 ] \cdot A [ 2 ] \cdots A [ n + 1 ] "$

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