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.
SwinnertonDyer 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: 0521568234 (quote from SwinnertonDyer and Euclidian example)
Dictionary.com  etymology of Lemma