# lemma

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## 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 Lemma 11 and [11, Corollaire 2] we have [h.sup.1] (N, [I.sub.C[intersection]N,N](t)) = 0 if t [greater than or equal to] 5 and the plane N contains neither a line R with deg(R [intersection] C) [greater than or equal to] t + 2 nor a conic D with deg(D [intersection] C) [greater than or equal to] 2t + 2.
Noticing that the measure [absolute value of {x [member of] B : [absolute value of [b, [T.sub.[OMEGA]]]u - [([b, [T.sub.[OMEGA]]]u).sub.B]] > 0}] > 0, we could use Lemma 6.
Moreover, by Lemma 2.2(ii), we may assume that [x'.sub.1] is sufficiently large such that for all x [greater than or equal to] [x'.sub.1] and all t > 0,
In a way similar to the proof of Lemma 13, we get that [mathematical expression not reproducible], which contradicts with the boundedness of f(x), x [member of] F.
By Lemma 7, G must be isomorphic to the sandglass graph S([C.sub.3], [P.sub.h], [C.sub.3]).
Then, by Lemma 8, we have g(r) > 0 for all r > 0 and g(r) [right arrow] +[infinity] as r [right arrow] +[infinity].
A particular case of Lemma 5 provides a constant C independent of w [member of] D such that
We know from [4, Lemma 1] that, for every n [greater than or equal to] 1, [G.sub.u,n] = [G.sub.[bar.u],n] if and only if u [equivalent to] [bar.u] mod n.
By Lemma 2.3 (3), then [[sigma].sub.l](A) is an infinite set and its elements are of the same modulus and real part.
* Step 4: Compute the new iterate [mathematical expression not reproducible] by Lemma 1 and [mathematical expression not reproducible].
and similarly [mathematical expression not reproducible], and by Lemma 14

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