Examples of using Lemma in English and their translations into Russian
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This lemma was introduced by Yegor Ivanovich Zolotarev in an 1872 proof of quadratic reciprocity.
Then by the lemma, the sum of S′ is strictly less than Fs+ 1 and so is strictly less than Ft, whereas the sum of T′ is clearly at least Ft.
This lemma, in turn, can be used to calculate the chromatic number of the Kneser graphs,
For this connection between Rado's lemma and the De Bruijn-Erdős theorem, see e.g. the discussion following Theorem A of Nash-Williams 1967.
The lemma was apparently so well known that Burnside simply omitted to attribute it to Cauchy.
In 2008, Ngô Bảo Châu proved the"fundamental lemma", which was originally conjectured by Langlands in 1983
By Berge's lemma, matching M is maximum if and only if there
The handshaking lemma is also used in proofs of Sperner's lemma and of the piecewise linear case of the mountain climbing problem.
Lemma Senbet, Professor of Finance, Department of Economics, University of Maryland;
Hough used the Lovász local lemma to show that there is some maximum N.
In this case, an argument based on Kőnig's lemma can be used to show that there exists a tessellation of the whole plane by congruent copies of the tile.
The existence of a property on a random graph can often imply, via the Szemerédi regularity lemma, the existence of that property on almost all graphs.
making Schur's lemma applicable.
Kazimierz Kuratowski proved in 1922 a version of the lemma close to its modern formulation it applies to sets ordered by inclusion and closed under unions of well-ordered chains.
Papakyriakopoulos is best known for his proofs of Dehn's lemma, the loop theorem,
Nash-Williams(1967) gives a proof for graphs with a countable number of vertices based on Kőnig's infinity lemma.
Let us now prove the contrapositive of Berge's lemma: G has a matching larger than M if
But this alternative construction is useless in the proof of Lemma 2.2. V, so we do not present it in the paper.
also be shown to be equivalent in axiomatic power, within a theory of second-order arithmetic, to Kőnig's infinity lemma.
Grünbaum attributes the key lemma in this result, that every set of d+ 3 points contains the vertices of a(d+ 2)-vertex cyclic polytope, to Micha Perles.