What is a lemma?

A proven statement used as a stepping-stone toward the proof of another statement is called lemma.

For example:

Euclid’s Division Lemma: Let a and b be any two positive integers.

Then, there exist unique integers q and r such that 

$a=b q+r, 0 \leq r

If $b \mid a$ then $r=0$.

Otherwise, $r$ satisfies the stronger inequality $0