1. The Johnson–Lindenstrauss lemma is a classic result in this vein.

2. Lemma: Two Cosets of are either identical or nonintersecting.

3. This problem became known as the Fundamental Lemma .

4. Each Coset has exactly jHj elements by the previous lemma

5. The lemma is named after the mathematician Pavel Samuilovich Urysohn.

6. Advanced mathematical proofs like Siegel's lemma build upon this more general concept.

7. The notion of exact sequence is meaningful in Grp, and some results from the theory of abelian categories, such as the nine lemma, the five lemma, and their consequences hold true in Grp.

8. Urysohn's lemma is commonly used to construct continuous functions with various properties on normal spaces.

9. The five lemma is not only valid for abelian categories but also works in the category of groups, for example.

10. In the following example, the lexical entry is associated with a lemma clergyman and two inflected forms clergyman and clergymen.

11. This we handle in Lemma 8, which Arithmetizes the low amortized free bits PCP of [12] (using principles taken from [8])

12. Corollary: It’s far easier to understand what a Corollary is than it is to understand what a theorem and a lemma are

13. A Corollary is a theorem that follows on from another theorem A Lemma is a small result (less important than a theorem)

14. The snake lemma is valid in every abelian category and is a crucial tool in homological algebra and its applications, for instance in algebraic topology.

15. Binegation is generally put in fourth position, but in putting it in third, I follow YAMAUCHI Tokury, Rogosu to renma (Logos and lemma), Tokyo, Iwanami, 1974

16. The proof that left Adjoints are right-exact, and that right Adjoints are left-exact, uses a small incarnation of Yoneda’s Lemma, and illustrates the importance of naturality of isomorphisms

17. We show an almost optimal effective version of Masser’s matrix lemma (Lecture Notes Math. 1290:109–148, 1987), giving a lower bound of the height of an abelian variety in terms of its period lattices.

18. Paul Garrett: Adjoints, naturality, exactness, small Yoneda lemma (October 24, 2014) Given a -module M, MI is a -module with a -module map j: MI!M through which every map N!Mfrom an I-null -module Nfactors

19. Lemma 11 (Kahrobaei [6]) Suppose [phi] : A [right arrow] B is an isomorphism between two groups A and B: Let C < A; and let D be the amalgamated product of A and B Amalgamating C with C[phi]:

20. Leaf: ligule 1.5--3 mm, truncate to obtuse, decurrent to sheath, toothed; blade 1--5 mm, 1--2 mm wide, flat or folded.Inflorescence: 4--14 cm, 0.5--1.5 cm wide, narrow; branches Appressed, loosely flowered.Spikelet: in lower branch axils cleistogamous, enclosed by tightly rolled sheath; glumes 1--2 mm, obtuse to acute; lemma 4.5--6 mm, hairs at base short