Sometimes a lemma is used to prove a theorem. First we prove the lemma then use it to prove the theorem. But what is the difference between theorem and lemma?
Octav Olteanu
A lemma is usually a result which is applied in order to prove a more general and elaborated result, that is one or more theorems. Examples: Urysohn's lemma in C^(infinity) is used in proving that any positive distribution is the restriction of a positive measure to the subspace of test - functions; Schwarz lemma is a basic result in analytic complex functions field. It helps in proving related optimization results, which represent theorems. A lemma could be also an important result in itself.
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