A Lemma (from the greek word "lambanein", to take) is a central idea in Mathematics. As a general rule, the results of a Lemma constitute a Theorem. Although both a Lemma or an Axiom are taken to be true and can be used when proving a theory, an axiom is self evident, whereas a Lemma must first be proven.

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

Lem"ma (?), n.; pl. L. Lemmata (#), E. Lemmas (#). [L. lemma, Gr. anything received, an assumption or promise taken for granted, fr. to take, assume, Cf. Syllable.]

A preliminary or auxiliary proposition demonstrated or accepted for immediate use in the demonstration of some other proposition, as in mathematics or logic.

Log in or register to write something here or to contact authors.