Prove the correctness of the following sorting algorithm.

function sort (A : list[1 . . . n])

var int i, j

for i from n to 1

for j from 1 to i 1

if (A[j] > A[j + 1])

swap the values of A[j] and A[j + 1]

Use mathematical reasoning, such as mathematical induction, to prove the algorithms correctness.