# lemma

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Related to lemmas: lemmata

## lemma

(lĕm`ə): see theoremtheorem,
in mathematics and logic, statement in words or symbols that can be established by means of deductive logic; it differs from an axiom in that a proof is required for its acceptance.
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## lemma

[′lem·ə]
(botany)
Either of the pair of bracts that are borne above the glumes and enclose the flower of a grass spikelet.
(mathematics)
A mathematical fact germane to the proof of some theorem.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.

## lemma

(logic)
A result already proved, which is needed in the proof of some further result.
References in periodicals archive ?
By Lemmas 8 and 10 we proved the part of Theorem 1 concerning non-degenerate C [member of] [M.sub.d,g].
From Lemma 2, properties of modulus, and Holder's inequality, we have
Combining Lemmas 9 and 10, we have the following result.
To prove the left hand side inequality in (4.8), using Lemmas 4 and 6 and Corollary 2, we derive
Then, by using Lemma 1, we get S(RL] = (SS](.RL] [subset or equal to] (SS * RL] = (SR * SL] [subset or equal to] (SR * (SL]] = (SR * L] = ((SS]R * L] [subset or equal to] ((SS)R * L] = ((RS)S * L] [subset or equal to] ((RS]S * L] [subset or equal to] (RL], which shows that (RL] is a left ideal of S.
Applying Lemmas 4 and 2 to [b, [T.sub.[OMEGA]]]u with any s, p > 0, we have
By Lemma 2, the last inequality is due to the fact the function [f.sub.2](x) = x/(2/x + A) - (x - 1)/(2/(x - 1) + A) for x [greater than or equal to] 2 and 0 < A [less than or equal to] 3 is an increasing function.
The following Lemma is due to Lemma 3.3 of Leipus and Siaulys (2007).
Lemma 5 will be used to develop test functions needed for the proof of the converse.
Two lemmas below, edge conditions for [F.sub.u,n] and [[??].sub.u,n], are the useful results obtained in [1] and [3], respectively.

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