Inmathematics and other fields,[a] alemma (pl.:lemmas orlemmata) is a generally minor,provenproposition which is used to prove a larger statement. For that reason, it is also known as a "helpingtheorem" or an "auxiliary theorem".[3][4] 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.[5]
From theAncient Greek λῆμμα, (perfect passive εἴλημμαι) something received or taken. Thus something taken for granted in an argument.[6]
There is no formal distinction between a lemma and atheorem, only one of intention (seeTheorem terminology). However, a lemma can be considered a minor result whose sole purpose is to help prove a more substantial theorem – a step in the direction of proof.[5]
Some powerful results in mathematics are known as lemmas, first named for their originally minor purpose. These include, among others:
While these results originally seemed too simple or too technical to warrant independent interest, they have eventually turned out to be central to the theories in which they occur.
This article incorporates material from Lemma onPlanetMath, which is licensed under theCreative Commons Attribution/Share-Alike License.
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