Q: How to classify the statement "If $n=a\cdot b$ and $a\leq b$, then $a\cdot a \leq a\cdot b = n$"? A property? inequality? formula? other? This is some algebra used to help write a prime finder from an SO Q/A comment:

because if n = a * b and a <= b then a * a <= a * b = n.
– Will Ness Mar 1 '14 at 4:35

It is used to create this code here:
// j <= Math.sqrt(i)
for(let j = 2; j * j <= i; j++){

However I was trying to classify this "truth".
I looked at various cheat sheets such as this one, and could not find any direct references to it.
The closest was the Radical Properties section. Is there a name for the algebraic formula above.

How is it classified ... a property?  An equality? A formula? A derivation?

There is no algebra tag for this site?

A: I think what you're looking for is that this is a defining axiom for an ordered ring
Specifically, if $c\geq 0$ and $a\leq b$, then $ac\leq bc$.  In your case I guess you are assuming $c=a\geq 0$.
There is of course a notion of ordered group too but since it looked like you were basically using integers, I chose that one above.
The definition given in wikipedia for an ordered semigroup would be a particularly good fit if you were just considering $\mathbb N$, but I'm not familiar with it. (I'm surprised there's no positivity condition mentioned.)
