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.

Algebra

 * Abhyankar's lemma
 * Aubin–Lions lemma
 * Bergman's diamond lemma
 * Fitting lemma
 * Injective test lemma
 * Hua's lemma (exponential sums)
 * Krull's separation lemma
 * Schanuel's lemma (projective modules)
 * Schwartz–Zippel lemma
 * Shapiro's lemma
 * Stewart–Walker lemma (tensors)
 * Whitehead's lemma (Lie algebras)
 * Zariski's lemma

Algebraic geometry

 * Abhyankar's lemma
 * Fundamental lemma (Langlands program)

Category theory

 * Five lemma
 * Horseshoe lemma
 * Nine lemma
 * Short five lemma
 * Snake lemma
 * Splitting lemma

Linear algebra

 * Matrix determinant lemma
 * Matrix inversion lemma

Group theory

 * Burnside's lemma also known as the Cauchy–Frobenius lemma
 * Frattini's lemma (finite groups)
 * Goursat's lemma
 * Mautner's lemma (representation theory)
 * Ping-pong lemma (geometric group theory)
 * Schreier's subgroup lemma
 * Schur's lemma (representation theory)
 * Zassenhaus lemma

Polynomials

 * Gauss's lemma (polynomials)
 * Schwartz–Zippel lemma

Ring theory and commutative algebra

 * Artin–Rees lemma
 * Hensel's lemma (commutative rings)
 * Nakayama lemma
 * Noether's normalization lemma
 * Prime avoidance lemma

Universal algebra

 * Jónsson's lemma

Analysis

 * Fekete's lemma
 * Fundamental lemma of calculus of variations
 * Hopf lemma
 * Sard's lemma (singularity theory)
 * Stechkin's lemma (functional and numerical analysis)
 * Vitali covering lemma (real analysis)
 * Watson's lemma

Complex analysis

 * Estimation lemma (contour integrals)
 * Hartogs's lemma (several complex variables)
 * Jordan's lemma
 * Lemma on the Logarithmic derivative
 * Schwarz lemma

Fourier analysis

 * Riemann–Lebesgue lemma

Differential equations

 * Borel's lemma (partial differential equations)
 * Grönwall's lemma
 * Lax–Milgram lemma
 * Pugh's closing lemma
 * Weyl's lemma (Laplace equation) (partial differential equations)

Differential forms

 * Poincaré lemma of closed and exact differential forms

Functional analysis

 * Cotlar–Stein lemma
 * Ehrling's lemma
 * Riesz's lemma

Mathematical series

 * Abel's lemma
 * Kronecker's lemma

Numerical analysis

 * Bramble–Hilbert lemma
 * Céa's lemma

Applied mathematics

 * Danielson–Lanczos lemma (Fourier transforms)
 * Farkas's lemma (linear programming)
 * Feld–Tai lemma (electromagnetism)
 * Little's lemma (queuing theory)
 * Finsler's lemma

Control theory

 * Finsler's lemma
 * Hautus lemma
 * Kalman–Yakubovich–Popov lemma

Computational complexity theory

 * Isolation lemma
 * Switching lemma

Cryptography

 * Forking lemma
 * Leftover hash lemma
 * Piling-up lemma (linear cryptanalysis)
 * Yao's XOR lemma

Formal languages

 * Interchange lemma
 * Newman's lemma (term rewriting)
 * Ogden's lemma
 * Pumping lemma sometimes called the Bar-Hillel lemma

Microeconomics

 * Hotelling's lemma
 * Shephard's lemma

Combinatorics

 * Cousin's lemma (integrals)
 * Dickson's lemma
 * Littlewood–Offord lemma
 * Pólya–Burnside lemma
 * Sperner's lemma
 * Ky Fan lemma (combinatorial geometry)

Graph theory

 * Berge's lemma
 * Counting lemma
 * Crossing lemma
 * Expander mixing lemma
 * Handshaking lemma
 * Kelly's lemma
 * Kőnig's lemma
 * Szemerédi regularity lemma

Order theory

 * Higman's lemma
 * Ultrafilter lemma

Dynamical systems

 * Barbalat's lemma
 * Kac's lemma (ergodic theory)

Geometry

 * Shadowing lemma
 * Big-little-big lemma (mathematics of paper folding)
 * Gordan's lemma
 * Hilbert's lemma

Euclidean geometry

 * Archimedes's lemmas
 * Johnson–Lindenstrauss lemma (Euclidean geometry)

Hyperbolic geometry

 * Margulis lemma

Metric spaces

 * Lebesgue's number lemma (dimension theory)

Riemannian geometry

 * Gauss's lemma (Riemannian geometry)

Mathematical logic

 * Craig interpolation lemma
 * Diagonal lemma
 * Lindenbaum's lemma
 * Mostowski collapse lemma
 * Teichmüller–Tukey lemma also known as Tukey's lemma
 * Zorn's lemma; equivalent to the axiom of choice

Set theory

 * Covering lemma
 * Delta lemma
 * Dynkin lemma
 * Fodor's lemma
 * Fixed-point lemma for normal functions (axiomatic set theory)
 * Moschovakis coding lemma
 * Rasiowa–Sikorski lemma

Number theory

 * Bézout's lemma
 * Dwork's lemma
 * Euclid's lemma
 * Gauss's lemma
 * Hensel's lemma
 * Zolotarev's lemma
 * Siegel's lemma (Diophantine approximation)

Analytic number theory

 * Hua's lemma
 * Vaughan's lemma

Diophantine equations

 * Bhaskara's lemma

Sieve theory

 * Fundamental lemma of sieve theory

Probability theory

 * Borel–Cantelli lemma
 * Doob–Dynkin lemma
 * Itô's lemma (stochastic calculus)
 * Lovász local lemma
 * Stein's lemma
 * Wald's lemma

Statistics

 * Glivenko–Cantelli lemma
 * Neyman–Pearson lemma
 * Robbins lemma

Measure theory

 * Factorization lemma
 * Fatou's lemma
 * Frostman's lemma (geometric measure theory)
 * Malliavin's absolute continuity lemma

Topology

 * Lindelöf's lemma
 * Urysohn's lemma
 * Tube lemma

Differential topology

 * Morse lemma

Fixed-point theory

 * Knaster–Kuratowski–Mazurkiewicz lemma

Geometric topology

 * Dehn's lemma

Topological groups and semigroups

 * Ellis–Numakura lemma (topological semigroups)