Swinnerton-Dyer observes that […] anyone who can prove a theorem can have it named after them, but 'It is the height of distinction to have a lemma named after you'.- The Pleasures of Counting, T. W. Körner

For example, Euclid's algorithm finds the greatest common divisor of two integers, and is based upon this Lemma:

**Suppose:**

*m = qn + r*where m and n are integers with m

__<__n

__<__1 and that q and r are integers with q

__<__r

__<__0.

**then**

greatest_common_divisor(m,n) = greatest_common_divisor(n,r)

Sources: "The Pleasures of Counting" by T. W. Körner ISBN: 0-521-56823-4 (quote from Swinnerton-Dyer and Euclidian example)

Dictionary.com - etymology of Lemma