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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Definitions:

Nucleic Acids

Biomolecules essential for all known forms of life, which include DNA and RNA, responsible for storing and transmitting genetic information.

Enterokinase

Intestinal proteolytic enzyme that converts trypsinogen into trypsin.

Trypsinogen

An inactive enzyme precursor produced in the pancreas, that, once activated to trypsin, plays a key role in the digestion of proteins in the small intestine.

Cholecystokinin

Cholecystokinin is a hormone produced by the cells of the duodenum, involved in stimulating the digestion of fat and protein by triggering the gallbladder to release bile and the pancreas to secrete enzymes.