List of lemmas

This following is a list of lemmas (or, "lemmata", i.e. minor theorems, or sometimes intermediate technical results factored out of proofs). See also list of axioms, list of theorems and list of conjectures.

0 to 9

*0/1 Sorting Lemma ("comparison-exchange algorithms")

A to E

*Abel's lemma ("mathematical series")
*Abhyankar's lemma ("algebraic geometry")
*Archimedes' lemmas ("euclidean geometry")
*Artin-Rees lemma ("commutative algebra") "named after Emil Artin and Elmer Rees"
*Aubin-Lions lemma
*Barbalat's lemma ("dynamical systems)
*Basic perturbation lemma ("computer science, algebra")
*Berge's lemma ("graph theory") "named after Claude Berge"
*Bézout's lemma ("number theory")
*Bhaskara's lemma ("Diophantine equations)
*Borel's lemma ("partial differential equations)
*Borel-Cantelli lemma ("probability theory")
*Bounding lemmas, "of which there are several"
*Bramble-Hilbert lemma ("numerical analysis")
*Brezis-Lions lemma
*Burnside's lemma "also known as the Cauchy-Frobenius lemma" ("group theory")
*Céa's lemma ("numerical analysis")
*Closed map lemma ("topology")
*Closeness lemma ("functions")
*Commutation lemmas, "of which there are several"
*Composition lemmas, "of which there are several"
*Cotlar–Stein lemma ("functional analysis")
*Counting lemmas, "of which there are several"
*Cousin's lemma ("gauge theory, integrals)
*Covering lemma ("set theory")
*Craig interpolation lemma ("mathematical logic")
*Crossing lemma ("knot theory, graph theory")
*Danielson-Lanczos lemma ("Fourier transforms)
*Davis-Figiel-Johnson-Pelczynski factorization lemma
*Dehn's lemma ("geometric topology")
*Delta lemma ("set theory")
*Deny-Lions lemma
*Diagonal lemma ("mathematical logic")
*Dickson's lemma ("combinatorics")
*Dobrushin's lemma ("point process theory")
*Dwork's lemma ("number theory")
*Dynkin lemma ("set theory")
*Ehrling's lemma ("functional analysis")
*Ellis–Nakamura lemma ("topological semigroups")
*Estimation lemma ("contour integrals)
*Euclid's lemma ("number theory")
*Expander mixing lemma ("graph theory")
*Expansion lemmas, "of which there are several"

F to J

*Factorization lemma ("measure theory")
*Farkas's lemma ("nonlinear programming")
*Fatou's lemma ("measure theory")
*Feinstein's fundamental lemma ("probability theory")
*Fekete's lemma ("mathematical analysis")
*Feld-Tai lemma ("electromagnetism")
*Finsler's lemma ("control theory")
*Fitting lemma ("abstract algebra")
*Five lemma ("homological algebra")
*Fixed-point lemma for normal functions ("axiomatic set theory")
*Fodor's lemma ("set theory")
*Forking lemma ("cryptography")
*Frattini's lemma ("finite groups")
*Friedrichs' lemma
*Frostman's lemma ("geometric measure theory")
*Fundamental lemma of calculus of variations
*Fundamental lemma of interpolation theory ("numerical analysis")
*Fundamental lemma of sieve theory ("sieve theory")
*Gauss's lemmas ("polynomials" | "number theory" | "Riemannian geometry")
*Glivenko-Cantelli lemma ("statistics")
*Gödel's diagonal lemma ("mathematical logic")
*Goursat's lemma ("algebra")
*Grönwall's inequality "Grönwall's lemma" ("inequalities")
*Gromov's convex integration lemma
*Gross's integration lemma
*Grothendieck lemma ("differential forms) named after Alexander Grothendieck
*Handshaking lemma ("graph theory")
*Hardy-Littlewood lemma ("differentiation")
*Harmonic series summation lemma
*Haruki's lemma ("plane geometry")
*Hartogs' lemma ("several complex variables")
*Hayashi's connecting lemma
*Hensel's lemma ("commutative rings")
*Higman's lemma ("order theory")
*Hindley-Rosen lemma
*Horseshoe lemma ("homological algebra")
*Hotelling's lemma ("envelope theory microeconomics)
*Hua's lemma ("analytic number theory")
*Huet's strong confluence lemma
*Injective test lemma ("homological algebra")
*Integration lemmas, "of which there are several"
*Iteration lemmas, "of which there are several"
*Itō's lemma ("stochastic calculus")
*Johnson-Lindenstrauss lemma ("Euclidean geometry")
*Jordan's lemma ("complex analysis")

K to O

*Kalman-Yakubovich-Popov lemma ("system analysis, control theory")
*Kelly's lemma ("graph theory")
*Klop's lemma ("lambda calculus")
*Knaster-Kuratowski-Mazurkiewicz lemma ("fixed-point theory")
*Knuth's 0-1 sorting lemma
*König's lemma ("graph theory}
*Kronecker's lemma ("infinite sums)
*Krull's separation lemma
*Lambda lemma "for normally hyperbolic invariant manifolds" ("topology")
*Lax-Milgram lemma ("differential equations")
*Lebesgue's number lemma ("dimension theory")
*Leftover hash-lemma ("cryptography")
*Lindelöf's lemma ("topology")
*Lindenbaum's lemma ("mathematical logic")
*Lions' lemma
*Little's lemma ("queuing theory")
*Littlewood-Offord lemma ("combinatorics")
*Lojasiewicz factorization lemma
*Lovász local lemma ("probability theory")
*Margulis lemma ("hyperbolic geometry")
*Matrix determinant lemma ("matrix theory")
*Matrix inversion lemma
*Mautner's lemma ("representation theory")
*Morse lemma ("differential topology")
*Moschovakis' coding lemma ("set theory")
*Mostowski collapse lemma ("mathematical logic")
*Nakayama lemma ("commutative algebra")
*Newman's lemma ("term rewriting")
*Neyman-Pearson lemma ("statistics")
*Nine lemma ("homological algebra")
*Noether's normalization lemma ("commutative algebra")
*Ogden's lemma ("formal languages")

P to T

*Parallel moves lemma
*Parity lemmas, "of which there are several"
*Partition lemmas, "of which there are several"
*Ping-pong lemma ("geometric group theory")
*Piling-up lemma ("linear cryptanalysis")
*Poincaré lemma of closed and exact differential forms ("differential forms)
*Pólya-Burnside lemma
*Pugh's closing lemma
*Pumping lemma ("formal languages) sometimes called the Bar-Hillel lemma"
*Quantifier reversal lemma
*Racah factorization lemma
*Rasiowa-Sikorski lemma ("set theory")
*Recursion lemmas, "of which there are several"
*Reduction lemmas, "of which there are several"
*Ricci's lemma ("tensors)
*Riemann-Lebesgue lemma ("harmonic analysis")
*Rigidity lemma ("algebraic geometry")
*Riesz's lemma ("functional analysis")
*Rouche-Kronecker-Campelli lemma ("linear algebra")
*Sard's lemma ("mathematical analysis, singularity theory")
*Satisfiability coding lemma
*Schanuel's lemma ("projective modules)
*Schreier's subgroup lemma ("group theory")
*Schur's lemma ("representation theory")
*Schwarz lemma ("complex analysis")
*Schwartz-Zippel lemma ("polynomials)
*Separation lemmas, "of which there are several"
*Shadowing lemma ("geometry")
*Shephard's lemma ("microeconomics")
*Short five lemma ("homological algebra")
*Siegel's lemma ("Diophantine approximation")
*Snake lemma ("homological algebra")
*Sperner's lemma ("combinatorics")
*Splitting lemma ("homological algebra")
*Stein's lemma ("probability theory")
*Stewart-Walker lemma ("tensors)
*Szemerédi regularity lemma ("graph theory")
*Transformation lemmas, "of which there are several"
*Tube lemma ("topology")
*Tukey's lemma ("metamathematics") "also known as the" Teichmüller-Tukey lemma

U to Z

*Ultrafilter lemma ("order theory")
*Uniform bounding lemma
*Urysohn's lemma ("general topology")
*Varadhan's integration lemma
*Vaughan's lemma ("analytic number theory")
*Verdu-Han lemma ("probability theory")
*Vitali covering lemma ("real analysis")
*Vizing's adjacency lemma ("graph theory")
*Wald's lemma ("probability theory")
*Weyl's lemma (Laplace equation) ("partial differential equations")
*Whitehead's lemma ("Lie algebras)
*Yao's XOR lemma ("cryptography")
*Yoneda lemma, ("category theory")
*Zassenhaus lemma ("group theory")
*Zolotarev's lemma ("number theory")
*Zorn's lemma "also known as the Kuratowski-Zorn lemma" ("set theory")