For the following algorithms, describe the loop invariant$($s$)$ and prove that they are sound and complete.

$($a$)$

Algorithm $1$: findMin

Input: a: A non$-$empty array of integers $($indexed starting at $1)$

Output: The smallest element in the array

begin

min $\backslash$infty

for i $1$ to len$($a$)$ do