# lemma

## Definitions

• WordNet 3.6
• n lemma the heading that indicates the subject of an annotation or a literary composition or a dictionary entry
• n lemma a subsidiary proposition that is assumed to be true in order to prove another proposition
• n lemma the lower and stouter of the two glumes immediately enclosing the floret in most Gramineae
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Webster's Revised Unabridged Dictionary
• Lemma (Math., Logic) A preliminary or auxiliary proposition demonstrated or accepted for immediate use in the demonstration of some other proposition, as in mathematics or logic.
• Lemma A word that is included in a glossary or list of headwords; a headword.
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Century Dictionary and Cyclopedia
• n lemma In logic:
• n lemma In the Stoical logic
• n lemma The major premise of a hypothetical syllogism, or modus ponens: thus, in the reasoning, “If it is day, it is light; but it is day: hence, it is light,” the first premise was called the lemma.
• n lemma A premise in general.
• n lemma A Megaric sophism depending on the question whether a man who says “I am lying” is truly lying or not.
• n lemma In mathematics, a proposition upon which it is necessary to arrest the attention for the sake of proving an ulterior one, but which interrupts the regular series of theorems; also, a premise drawn from another branch of mathematics than that under consideration.
• n lemma A theme; a thesis; the subject of an epigram, or of a musical composition, etc.
• n lemma In embryology, the primary or outer layer of the germinal vesicle. Pascoe. Synonyms See inference.
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Chambers's Twentieth Century Dictionary
• n Lemma lem′a (math.) a preliminary proposition demonstrated for the purpose of being used in a subsequent proposition: sometimes in logic a premise taken for granted: a theme
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## Etymology

Webster's Revised Unabridged Dictionary
L. lemma, Gr. lh^mma anything received, an assumption or premise taken for granted, fr. lamba`nein to take, assume. Cf. Syllable
Chambers's Twentieth Century Dictionary
L.,—Gr. lēmmalambanein, to take.

## Usage

### In literature:

This postulate or axiom rests on Postulate i. and Lemmas v. and vii., which see after II.
"The Ethics" by Benedict de Spinoza
LEMMA, subject proposed, or title of the epigram.
"Volpone; Or, The Fox" by Ben Jonson
LEMMA, subject proposed, or title of the epigram.
"The Alchemist" by Ben Jonson
LEMMA, subject proposed, or title of the epigram.
"The Poetaster" by Ben Jonson
LEMMA, subject proposed, or title of the epigram.
"Sejanus: His Fall" by Ben Jonson
LEMMA, subject proposed, or title of the epigram.
"Every Man In His Humor" by Ben Jonson
Above the glumes are two or more other bracts, the lemmas.
"The Plants of Michigan" by Henry Allan Gleason
The proof in this and in all cases depends on a lemma which forms Prop.
"Archimedes" by Thomas Little Heath
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### In news:

Lemma 's formula is little Quiz Bowl, all rock 'n' roll.
Lemma is two full-time musicians, a doctoral student and an abstract geometry researcher.
Lemma 's formula is little Quiz.
Abey Belette Girma, 37, is wanted on a capital murder warrant accusing him of killing Yayehyirad "Yared" Lemma, 40.
Jennifer Lemma for The Walla Walla Valley Weekly.
Abey Girma (Dallas County Sheriff 's Department) It's been three months since 40-year-old Yayehyirad "Yared" Lemma and 31-year-old Yenenesh "Yenni" Desta were shot to death in front of their Lower Greenville home.
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### In science:

Lemmas 5 and the proof of Lemma 4 show that Silverberg’s general result can be improved in the special case where k is ﬁnite.
On the existence of absolutely simple abelian varieties of a given dimension over an arbitrary field
Thus we can sum up the the arguments of [NS] and [Su] (see also [Fa]) into a lemma Lemma 1.4.
Factorization of generalized theta functions at reducible case
But Lemma 2.6 in [Su] is not correct, we have to prove it without using the lemma (also to ﬁx the gap in [Su]).
Factorization of generalized theta functions at reducible case
The above Lemma 3.6 tells us that the assumption (surjectivity) in Lemma 3.5 is satisﬁed for the situation: V = Wa , eV = D1 (a), σ = φ|D1 (a) and N = ΘUX |Wa .
Factorization of generalized theta functions at reducible case
Notice that πρ · I in the lemma above is exactly the value of bP (ρ) in Lemma 2.5.1.
Random walks on wreath products of groups
Proof of this lemma is very similar to the proof of Lemma 6 and we will skip it.
Gaussian Random Matrix Models for q-deformed Gaussian Random Variables
If there are exactly two (1, 1) horizontal curves in C then the lemma is clear since the curves cannot be tangent by Lemma 3.6.
Rational polynomials of simple type
The proof of the following Lemma is straightforward Lemma 2.
Hamiltonian symplectomorphisms and the Berry phase
We will also utilize the following lemma which has the same proof as Lemma 36 of .
On the mixing time of simple random walk on the super critical percolation cluster
The proof of this lemma is similar to that of lemma 3 in .
Drift and entropy growth for random walks on groups
In this section we will supply the proof of Lemma B.2; we use the notation introduced before the statement of the lemma.
Harmonic mean, random polynomials and stochastic matrices
On the other hand, the Lemma 2.2 garantees the convergence to the limit measure with the rate at least 1 > ΛT > ΛT (α) (by Lemma 4.3).
Perron-Frobenius spectrum for random maps and its approximation
For condition (v), notice that the extensions of D and DA from Lemma 2.3.(a) and Lemma 3.5.(a) record exactly the special entry a in the A∞ -bimodule A.
Infinity-Inner-Products on A-Infinity-Algebras
We obtain this in two regions, ﬁrstly in Lemma 3.3 over the tail, and then in Lemma 3.4 over the rest of the real line.
An information-theoretic Central Limit Theorem for finitely susceptible FKG systems
By Lemma 3.1 (ii), A is a C ∗ -algebra and by Lemma 3.1 (i), A contains On⋊αω G.
AF-embeddability of crossed products of Cuntz algebras
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