In mathematics and other fields, a lemma (: lemmas or lemmata) is a generally minor, proven proposition which is used to prove a larger statement. For that reason, it is also known as a "helping theorem" or an "auxiliary theorem". In many cases, a lemma derives its importance from the theorem it aims to prove; however, a lemma can also turn out to be more important than originally thought.
Etymology
From the Ancient Greek λῆμμα, (perfect passive εἴλημμαι) something received or taken. Thus, something taken for granted in an argument.
Comparison with theorem
There is no formal distinction between a lemma and a theorem, only one of intention (see ). A result is called a lemma when it is a minor result whose purpose is to help prove a more substantial theorem,